| Displaying 1-5 of 5 results found.
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1
1, 1, 1, 2, 1, 3, 1, 4, 1, 1, 11, 1, 13, 7, 1, 8, 1, 9, 19, 10, 1, 11, 13, 6, 25, 13, 1, 7, 11, 15, 1, 16, 1, 15, 13, 2, 37, 1, 11, 12, 41, 1, 25, 22, 1, 13, 47, 4, 11, 25, 1, 1, 19, 3, 55, 1, 13, 11, 59, 5, 61, 31, 1, 32, 1, 33, 67, 34, 69, 35, 61, 36, 1, 37, 13, 38, 59, 39, 25, 40, 81, 41, 11, 42, 1, 43, 87, 44, 55, 45, 91, 46, 1, 47, 19, 24, 97, 49, 1, 25, 13
FORMULA
Other identities. For all n >= 1:
CROSSREFS
Cf. A044918 (very likely gives the positions of all ones).
Reverse run lengths in binary expansions of terms of A063037: for n >= 0, a(n) is the unique k such that A063037(1+k) = A056539( A063037(1+n)).
+10
3
0, 1, 2, 3, 6, 5, 4, 7, 8, 11, 10, 9, 16, 17, 18, 15, 12, 13, 14, 19, 32, 23, 22, 21, 24, 31, 28, 27, 26, 29, 30, 25, 20, 33, 42, 49, 48, 43, 44, 47, 50, 41, 34, 37, 38, 53, 52, 39, 36, 35, 40, 51, 46, 45, 74, 75, 84, 65, 58, 59, 64, 85, 86, 63, 60, 57, 66, 83
COMMENTS
This sequence is a self-inverse permutation of the nonnegative integers.
EXAMPLE
For n = 42:
- the binary expansion of 86 is "1010110",
- reversing run lengths yields "1001010",
- this corresponds to 74 = A063037(1+34), - hence a(42) = 34.
PROG
(PARI) See Links section.
CROSSREFS
See A357523 for a similar sequence.
Reverse run lengths in binary expansions of terms of A166535: for n > 0, a(n) is the unique k such that A166535(k) = A056539( A166535(n)); a(0) = 0.
+10
3
0, 1, 2, 3, 6, 5, 4, 7, 14, 9, 10, 13, 12, 11, 8, 15, 20, 23, 24, 19, 16, 27, 26, 17, 18, 25, 22, 21, 40, 41, 46, 35, 32, 49, 50, 31, 36, 45, 42, 39, 28, 29, 38, 43, 44, 37, 30, 51, 48, 33, 34, 47, 88, 63, 62, 89, 94, 57, 68, 83, 80, 71, 54, 53, 72, 79, 84, 67
COMMENTS
This sequence is a self-inverse permutation of the nonnegative integers.
EXAMPLE
For n = 42:
- the binary expansion of 50 is "110010",
- reversing run lengths yields "101100",
- this corresponds to 44 = A166535(38), - hence a(42) = 38.
PROG
(PARI) See Links section.
CROSSREFS
See A357522 for a similar sequence.
Reverse run lengths in binary expansions of terms of A044813: for n > 0, a(n) is the unique k such that A044813(k) = A056539( A044813(n)); a(0) = 0.
+10
1
0, 1, 2, 4, 3, 5, 7, 6, 8, 12, 11, 10, 9, 13, 23, 18, 20, 22, 15, 21, 16, 19, 17, 14, 24, 36, 29, 33, 35, 26, 34, 32, 31, 27, 30, 28, 25, 37, 55, 44, 47, 49, 52, 54, 39, 53, 51, 40, 50, 41, 48, 46, 42, 45, 43, 38, 56, 82, 63, 68, 76, 79, 81, 58, 69, 73, 80, 78
COMMENTS
This sequence is a self-inverse permutation of the nonnegative integers.
EXAMPLE
For n = 42:
- the binary expansion of 159 is "10011111",
- reversing run lengths yields "11111001",
- this corresponds to 249 = A044813(52), - hence a(42) = 52.
PROG
(PARI) See Links section.
Reverse run lengths in binary expansions of terms of A031443: for n > 0, a(n) is the unique k such that A031443(k) = A056539( A031443(n)); a(0) = 0.
+10
1
0, 1, 2, 3, 4, 11, 8, 7, 6, 9, 12, 5, 10, 13, 14, 45, 41, 31, 18, 38, 28, 21, 22, 27, 37, 36, 26, 23, 20, 29, 39, 17, 32, 42, 46, 35, 25, 24, 19, 30, 40, 16, 33, 43, 47, 15, 34, 44, 48, 49, 170, 165, 150, 115, 54, 161, 146, 111, 58, 136, 101, 68, 81, 88, 123
COMMENTS
This sequence is a self-inverse permutation of the nonnegative integers.
EXAMPLE
For n = 42:
- the binary expansion of 210 is "11010010",
- reversing run lengths yields "10110100",
- this corresponds to 180 = A031443(33), - hence a(42) = 33.
PROG
(PARI) See Links section.
CROSSREFS
See A057164 for a similar sequence.
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