Displaying 1-10 of 20 results found.
Smallest number whose cube has n digits.
+10
28
1, 3, 5, 10, 22, 47, 100, 216, 465, 1000, 2155, 4642, 10000, 21545, 46416, 100000, 215444, 464159, 1000000, 2154435, 4641589, 10000000, 21544347, 46415889, 100000000, 215443470, 464158884, 1000000000, 2154434691, 4641588834
COMMENTS
With offset 0, ((cube root of 10) to the power n) rounded up.
The terms corresponding to n = (20,21); (38,39); (41,42); (56,57); (59,60); (77,78); (80,81) ... are such that the square of first term starts with the digits of second term, and the square of second term starts with the digits of the first. For example, a(38)^2 = 2154434690032^2 = 4641588833613.... and a(39)^2 = 4641588833613^2 = 2154434690032...
(End)
EXAMPLE
a(5) = 22, 22^3 = 10648 has 5 digits, while 21^3 = 9261 has 4 digits.
CROSSREFS
Cf. A061434, A061439, and powers of cube root of k ceiling up: A017981 (k=2), A017984 (k=3), A017987 (k=4), A017990 (k=5), A017993 (k=6), A017996 (k=7), A018002 (k=9), this sequence (k=10), A018008 (k=11), A018011 (k=12), A018014 (k=13), A018017 (k=14), A018020 (k=15), A018023 (k=16), A018026 (k=17), A018029 (k=18), A018032 (k=19), A018035 (k=20), A018038 (k=21), A018041 (k=22), A018044 (k=23), A018047 (k=24).
EXTENSIONS
More terms from Larry Reeves (larryr(AT)acm.org), May 16 2001
Powers of cube root of 17 rounded up.
+10
23
1, 3, 7, 17, 44, 113, 289, 744, 1911, 4913, 12633, 32483, 83521, 214757, 552199, 1419857, 3650853, 9387369, 24137569, 62064487, 159585273, 410338673, 1055096276, 2712949631, 6975757441, 17936636689, 46120143717, 118587876497, 304922823712
MAPLE
Digits:= 1000:
a:= n-> ceil(17^(n/3)):
PROG
(PARI) a(n) = if (n % 3, ceil((17^(1/3))^n), 17^(n/3)); \\ Michel Marcus, Nov 23 2013
CROSSREFS
Cf. A010589, A018024, A018025, and powers of cube root of k ceiling up: A017981 (k=2), A017984 (k=3), A017987 (k=4), A017990 (k=5), A017993 (k=6), A017996 (k=7), A018002 (k=9), A018005 (k=10), A018008 (k=11), A018011 (k=12), A018014 (k=13), A018017 (k=14), A018020 (k=15), A018023 (k=16), this sequence (k=17), A018029 (k=18), A018032 (k=19), A018035 (k=20), A018038 (k=21), A018041 (k=22), A018044 (k=23), A018047 (k=24).
Powers of cube root of 3 rounded up.
+10
22
1, 2, 3, 3, 5, 7, 9, 13, 19, 27, 39, 57, 81, 117, 169, 243, 351, 506, 729, 1052, 1517, 2187, 3155, 4550, 6561, 9463, 13648, 19683, 28388, 40943, 59049, 85164, 122827, 177147, 255491, 368481, 531441, 766471, 1105442, 1594323, 2299412, 3316326, 4782969, 6898235
COMMENTS
Smallest integer such that a(n)^k-k^n is nonnegative for all nonnegative integers k. - Henry Bottomley, May 16 2005
CROSSREFS
Cf. A107586 and powers of cube root of k ceiling up: A017981 (k=2), this sequence (k=3), A017987 (k=4), A017990 (k=5), A017993 (k=6), A017996 (k=7), A018002 (k=9), A018005 (k=10), A018008 (k=11), A018011 (k=12), A018014 (k=13), A018017 (k=14), A018020 (k=15), A018023 (k=16), A018026 (k=17), A018029 (k=18), A018032 (k=19), A018035 (k=20), A018038 (k=21), A018041 (k=22), A018044 (k=23), A018047 (k=24).
Powers of cube root of 4 rounded up.
+10
21
1, 2, 3, 4, 7, 11, 16, 26, 41, 64, 102, 162, 256, 407, 646, 1024, 1626, 2581, 4096, 6502, 10322, 16384, 26008, 41286, 65536, 104032, 165141, 262144, 416128, 660562, 1048576, 1664511, 2642246, 4194304, 6658043, 10568984, 16777216, 26632171, 42275936, 67108864
CROSSREFS
Cf. powers of cube root of k ceiling up: A017981 (k=2), A017984 (k=3), this sequence (k=4), A017990 (k=5), A017993 (k=6), A017996 (k=7), A018002 (k=9), A018005 (k=10), A018008 (k=11), A018011 (k=12), A018014 (k=13), A018017 (k=14), A018020 (k=15), A018023 (k=16), A018026 (k=17), A018029 (k=18), A018032 (k=19), A018035 (k=20), A018038 (k=21), A018041 (k=22), A018044 (k=23), A018047 (k=24).
Powers of cube root of 6 rounded up.
+10
21
1, 2, 4, 6, 11, 20, 36, 66, 119, 216, 393, 714, 1296, 2355, 4280, 7776, 14130, 25676, 46656, 84780, 154055, 279936, 508678, 924329, 1679616, 3052065, 5545970, 10077696, 18312389, 33275820, 60466176, 109874334, 199654915, 362797056, 659246002
CROSSREFS
Cf. powers of cube root of k ceiling up: A017981 (k=2), A017984 (k=3), A017987 (k=4), A017990 (k=5), this sequence (k=6), A017996 (k=7), A018002 (k=9), A018005 (k=10), A018008 (k=11), A018011 (k=12), A018014 (k=13), A018017 (k=14), A018020 (k=15), A018023 (k=16), A018026 (k=17), A018029 (k=18), A018032 (k=19), A018035 (k=20), A018038 (k=21), A018041 (k=22), A018044 (k=23), A018047 (k=24).
Powers of cube root of 7 rounded up.
+10
21
1, 2, 4, 7, 14, 26, 49, 94, 180, 343, 657, 1256, 2401, 4593, 8786, 16807, 32151, 61502, 117649, 225055, 430514, 823543, 1575382, 3013596, 5764801, 11027668, 21095170, 40353607, 77193674, 147666185, 282475249, 540355713, 1033663292, 1977326743, 3782489986
CROSSREFS
Cf. powers of cube root of k ceiling up: A017981 (k=2), A017984 (k=3), A017987 (k=4), A017990 (k=5), A017993 (k=6), this sequence (k=7), A018002 (k=9), A018005 (k=10), A018008 (k=11), A018011 (k=12), A018014 (k=13), A018017 (k=14), A018020 (k=15), A018023 (k=16), A018026 (k=17), A018029 (k=18), A018032 (k=19), A018035 (k=20), A018038 (k=21), A018041 (k=22), A018044 (k=23), A018047 (k=24).
Powers of cube root of 9 rounded up.
+10
21
1, 3, 5, 9, 19, 39, 81, 169, 351, 729, 1517, 3155, 6561, 13648, 28388, 59049, 122827, 255491, 531441, 1105442, 2299412, 4782969, 9948977, 20694705, 43046721, 89540788, 186252345, 387420489, 805867092, 1676271102, 3486784401, 7252803827, 15086439913, 31381059609
CROSSREFS
Cf. powers of cube root of k ceiling up: A017981 (k=2), A017984 (k=3), A017987 (k=4), A017990 (k=5), A017993 (k=6), A017996 (k=7), this sequence (k=9), A018005 (k=10), A018008 (k=11), A018011 (k=12), A018014 (k=13), A018017 (k=14), A018020 (k=15), A018023 (k=16), A018026 (k=17), A018029 (k=18), A018032 (k=19), A018035 (k=20), A018038 (k=21), A018041 (k=22), A018044 (k=23), A018047 (k=24).
Powers of cube root of 12 rounded up.
+10
21
1, 3, 6, 12, 28, 63, 144, 330, 755, 1728, 3957, 9058, 20736, 47474, 108688, 248832, 569684, 1304249, 2985984, 6836197, 15650984, 35831808, 82034362, 187811805, 429981696, 984412343, 2253741659, 5159780352, 11812948115, 27044899908, 61917364224
CROSSREFS
Cf. powers of cube root of k ceiling up: A017981 (k=2), A017984 (k=3), A017987 (k=4), A017990 (k=5), A017993 (k=6), A017996 (k=7), A018002 (k=9), A018005 (k=10), A018008 (k=11), this sequence (k=12), A018014 (k=13), A018017 (k=14), A018020 (k=15), A018023 (k=16), A018026 (k=17), A018029 (k=18), A018032 (k=19), A018035 (k=20), A018038 (k=21), A018041 (k=22), A018044 (k=23), A018047 (k=24).
Powers of cube root of 13 rounded up.
+10
21
1, 3, 6, 13, 31, 72, 169, 398, 935, 2197, 5166, 12147, 28561, 67157, 157908, 371293, 873035, 2052796, 4826809, 11349444, 26686341, 62748517, 147542765, 346922421, 815730721, 1918055941, 4509991466, 10604499373, 24934727222, 58629889046, 137858491849
CROSSREFS
Cf. powers of cube root of k ceiling up: A017981 (k=2), A017984 (k=3), A017987 (k=4), A017990 (k=5), A017993 (k=6), A017996 (k=7), A018002 (k=9), A018005 (k=10), A018008 (k=11), A018011 (k=12), this sequence (k=13), A018017 (k=14), A018020 (k=15), A018023 (k=16), A018026 (k=17), A018029 (k=18), A018032 (k=19), A018035 (k=20), A018038 (k=21), A018041 (k=22), A018044 (k=23), A018047 (k=24).
Powers of cube root of 14 rounded up.
+10
21
1, 3, 6, 14, 34, 82, 196, 473, 1139, 2744, 6614, 15940, 38416, 92589, 223151, 537824, 1296233, 3124105, 7529536, 18147253, 43737462, 105413504, 254061542, 612324459, 1475789056, 3556861577, 8572542415, 20661046784, 49796062077, 120015593800, 289254654976
CROSSREFS
Cf. powers of cube root of k ceiling up: A017981 (k=2), A017984 (k=3), A017987 (k=4), A017990 (k=5), A017993 (k=6), A017996 (k=7), A018002 (k=9), A018005 (k=10), A018008 (k=11), A018011 (k=12), A018014 (k=13), this sequence (k=14), A018020 (k=15), A018023 (k=16), A018026 (k=17), A018029 (k=18), A018032 (k=19), A018035 (k=20), A018038 (k=21), A018041 (k=22), A018044 (k=23), A018047 (k=24).
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