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Search: a044918 -id:a044918
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a(n) = A280500(n,A280503(n)).
+10
4
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
OFFSET
1,4
FORMULA
a(n) = A280500(n,A280503(n)).
Other identities. For all n >= 1:
A048720(a(n), A280503(n)) = n.
PROG
(Scheme) (define (A280504 n) (A280500bi n (A280503 n))) ;; Code for A280500bi given in A280500.
CROSSREFS
Cf. A044918 (very likely gives the positions of all ones).
KEYWORD
nonn,base
AUTHOR
Antti Karttunen, Jan 09 2017
STATUS
approved
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
OFFSET
0,3
COMMENTS
This sequence is a self-inverse permutation of the nonnegative integers.
FORMULA
a(n) = n iff n = 0 or A044813(1+n) belongs to A044918.
EXAMPLE
For n = 42:
- A063037(1+42) = 86,
- 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.
KEYWORD
nonn,look,base
AUTHOR
Rémy Sigrist, Oct 02 2022
STATUS
approved
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
OFFSET
0,3
COMMENTS
This sequence is a self-inverse permutation of the nonnegative integers.
FORMULA
a(n) = n iff n = 0 or A166535(n) belongs to A044918.
EXAMPLE
For n = 42:
- A166535(42) = 50,
- 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.
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Oct 02 2022
STATUS
approved
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
OFFSET
0,3
COMMENTS
This sequence is a self-inverse permutation of the nonnegative integers.
FORMULA
a(n) = n iff n = 0 or A044813(n) belongs to A044918.
EXAMPLE
For n = 42:
- A044813(42) = 159,
- 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.
CROSSREFS
See A057164, A357522 and A357523 for similar sequences.
KEYWORD
nonn,look,base
AUTHOR
Rémy Sigrist, Oct 02 2022
STATUS
approved
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
OFFSET
0,3
COMMENTS
This sequence is a self-inverse permutation of the nonnegative integers.
FORMULA
a(n) = n iff n = 0 or A031443(n) belongs to A044918.
EXAMPLE
For n = 42:
- A031443(42) = 210,
- 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.
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Oct 02 2022
STATUS
approved

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