A007583 -id:A007583

A193652

A020988 and A007583 interleaved.

+20
7

0, 1, 2, 3, 10, 11, 42, 43, 170, 171, 682, 683, 2730, 2731, 10922, 10923, 43690, 43691, 174762, 174763, 699050, 699051, 2796202, 2796203, 11184810, 11184811, 44739242, 44739243, 178956970, 178956971, 715827882, 715827883, 2863311530, 2863311531, 11453246122

(list; graph; refs; listen; history; text; internal format)

COMMENTS

a(2*n) = A020988(n), a(2*n+1) = a(2*n) + 1 = A007583(n);

MAPLE

A007583(floor(n/2)) ;

A127961

a(n) = A007583(n) written in binary.

+20
6

1, 11, 1011, 101011, 10101011, 1010101011, 101010101011, 10101010101011, 1010101010101011, 101010101010101011, 10101010101010101011, 1010101010101010101011, 101010101010101010101011, 10101010101010101010101011, 1010101010101010101010101011

(list; graph; refs; listen; history; text; internal format)

EXAMPLE

A007583(2) = 11, which becomes 1011 when written in binary.

CROSSREFS

Cf. A007583.

A303009

Numbers n such that both A002450(n)=(2^(2n)-1)/3 and A007583(n)=2*A002450(n)+1 are Fermat pseudoprimes to base 2 (A001567).

+20
5

23, 29, 41, 53, 89, 113, 131, 179, 191, 233, 239, 251, 281, 293, 341, 359, 419, 431, 443, 491, 509, 593, 641, 653, 659, 683, 719, 743, 761, 809, 911, 953, 1013, 1019, 1031, 1049, 1103, 1223, 1229, 1271, 1289, 1409, 1439, 1451, 1481, 1499, 1511, 1559, 1583, 1601, 1733, 1811, 1889, 1901, 1931, 1973, 2003

(list; graph; refs; listen; history; text; internal format)

COMMENTS

(i) primes n such that 2n+1 is prime (cf. A005384) and A007583(n) is composite, with smallest such term n=a(1)=23;

(iii) 4-pseudoprimes n==5 (mod 6) such that 2n+1 is prime and A007583(n) is composite, with smallest such term n=a(15)=341;

(v) n=2k, where 4k is in A015921 and k==1 (mod 3), such that 2n+1 is prime and A007583(n) is composite, with the smallest such term n=67166;

CROSSREFS

Cf. A002450, A007583, A175625, A175942, A300193, A303008, A303447, A303448.

A115717

A divide-and-conquer triangle related to A007583.

+20
4

1, 0, 1, 3, -1, 1, 0, 0, 0, 1, 0, 4, -1, -1, 1, 0, 0, 0, 0, 0, 1, 12, -4, 4, 0, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 4, 0, 0, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 16, -4, -4, 4, 0, 0, 0, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 48, -16, 16, 0, -4, -4, 4, 0, 0, 0, 0, 0, -1, -1, 1

(list; graph; refs; listen; history; text; internal format)

CROSSREFS

Cf. A007583, A115715, A115716 (row sums), A167374.

A160156

Partial sums of A007583.

+20
4

1, 4, 15, 58, 229, 912, 3643, 14566, 58257, 233020, 932071, 3728274, 14913085, 59652328, 238609299, 954437182, 3817748713, 15270994836, 61083979327, 244335917290, 977343669141, 3909374676544, 15637498706155, 62549994824598

(list; graph; refs; listen; history; text; internal format)

CROSSREFS

Cf. A002450, A007583, A034299, A139250.

A166752

Interleave A007583 and A000012.

+20
2

1, 1, 3, 1, 11, 1, 43, 1, 171, 1, 683, 1, 2731, 1, 10923, 1, 43691, 1, 174763, 1, 699051, 1, 2796203, 1, 11184811, 1, 44739243, 1, 178956971, 1, 715827883, 1, 2863311531, 1, 11453246123, 1, 45812984491, 1, 183251937963, 1, 733007751851, 1

(list; graph; refs; listen; history; text; internal format)

A139784

a(4n+1)=2a(4n), a(4n+2)=2a(4n+1), a(4n+3)=2a(4n+2), a(4n+4)=2a(4n+3)+A007583(n).

+20
1

0, 0, 0, 0, 1, 2, 4, 8, 19, 38, 76, 152, 315, 630, 1260, 2520, 5083, 10166, 20332, 40664, 81499, 162998, 325996, 651992, 1304667, 2609334, 5218668, 10437336, 20877403, 41754806, 83509612, 167019224, 334049371, 668098742, 1336197484, 2672394968

(list; graph; refs; listen; history; text; internal format)

A131588

Interlaces A007583 with A083420.

+20
0

1, 1, 3, 7, 11, 31, 43, 127, 171, 511, 683, 2047, 2731, 8191, 10923, 32767, 43691, 131071, 174763, 524287, 699051, 2097151, 2796203, 8388607, 11184811, 33554431, 44739243, 134217727, 178956971, 536870911, 715827883, 2147483647, 2863311531

(list; graph; refs; listen; history; text; internal format)

CROSSREFS

Cf. A007583, A083420, A001045.

A000051

a(n) = 2^n + 1.
(Formerly M0717 N0266)

+10
849

2, 3, 5, 9, 17, 33, 65, 129, 257, 513, 1025, 2049, 4097, 8193, 16385, 32769, 65537, 131073, 262145, 524289, 1048577, 2097153, 4194305, 8388609, 16777217, 33554433, 67108865, 134217729, 268435457, 536870913, 1073741825, 2147483649, 4294967297, 8589934593

(list; graph; refs; listen; history; text; internal format)

FORMULA

a(n) = 3*A007583((n-1)/2) for n odd. - Eric W. Weisstein, Jul 17 2017

CROSSREFS

Cf. A007583 (a((n-1)/2)/3 for odd n).

Cf. A000079, A000225, A000918, A004119, A005126, A006217, A006521, A007583.

A001045

Jacobsthal sequence (or Jacobsthal numbers): a(n) = a(n-1) + 2*a(n-2), with a(0) = 0, a(1) = 1; also a(n) = nearest integer to 2^n/3.
(Formerly M2482 N0983)

+10
720

0, 1, 1, 3, 5, 11, 21, 43, 85, 171, 341, 683, 1365, 2731, 5461, 10923, 21845, 43691, 87381, 174763, 349525, 699051, 1398101, 2796203, 5592405, 11184811, 22369621, 44739243, 89478485, 178956971, 357913941, 715827883, 1431655765, 2863311531, 5726623061, 11453246123

(list; graph; refs; listen; history; text; internal format)

FORMULA

a(2*n) = A002450(n) = (4^n - 1)/3; a(2*n+1) = A007583(n) = (2^(2*n+1) + 1)/3. - Philippe Deléham, Mar 27 2004

CROSSREFS

Bisections: A002450, A007583.