cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A275845 Permutation of natural numbers: a(0) = 0, a(A153880(n)) = A255411(n), a(A273670(n)) = A256450(a(n)).

Original entry on oeis.org

0, 1, 4, 2, 6, 3, 12, 8, 16, 5, 15, 10, 18, 21, 22, 7, 20, 13, 24, 27, 28, 9, 26, 17, 48, 30, 52, 33, 34, 11, 60, 32, 64, 23, 56, 36, 66, 61, 70, 39, 40, 14, 73, 38, 78, 29, 67, 42, 72, 80, 76, 74, 85, 45, 84, 46, 88, 19, 89, 44, 90, 97, 94, 35, 81, 49, 87, 99, 93, 91, 105, 53, 96, 104, 100, 54, 109, 25, 108, 110, 112, 51, 111, 121, 114, 117, 118, 41
Offset: 0

Views

Author

Antti Karttunen, Aug 13 2016

Keywords

Crossrefs

Inverse: A275846.
Similar permutations: A273667 (a more recursed variant), A275847, A275848.

Formula

a(0) = 0; for n >= 1: if A257680(A225901(n)) = 0 [when n is one of the terms of A153880] then a(n) = A255411(A266193(n)), otherwise [when n is one of the terms of A273670], a(n) = A256450(a(A273663(n))).
Other identities:
a(A000142(n)) = A052849(n) for all n >= 2.

A275846 Permutation of natural numbers: a(0) = 0, a(A255411(n)) = A153880(n), a(A256450(n)) = A273670(a(n)).

Original entry on oeis.org

0, 1, 3, 5, 2, 9, 4, 15, 7, 21, 11, 29, 6, 17, 41, 10, 8, 23, 12, 57, 16, 13, 14, 33, 18, 77, 22, 19, 20, 45, 25, 101, 31, 27, 28, 63, 35, 129, 43, 39, 40, 87, 47, 165, 59, 53, 55, 111, 24, 65, 213, 81, 26, 71, 75, 141, 34, 89, 269, 105, 30, 37, 95, 99, 32, 183, 36, 46, 113, 341, 38, 135, 48, 42, 51, 119, 50, 125, 44, 231, 49, 64, 143, 431, 54, 52
Offset: 0

Views

Author

Antti Karttunen, Aug 13 2016

Keywords

Crossrefs

Inverse: A275845.
Similar permutations: A273668 (a more recursed variant), A275847, A275848.

Formula

a(0) = 0; for n >= 1: if A257680(n) = 0 [when n is one of the terms of A255411] then a(n) = A153880(A257684(n)), otherwise [when n is one of the terms of A256450], a(n) = A273670(a(A273662(n))).

A276082 a(0) = 0, a(2n) = A153880(a(n)), a(2n+1) = 1+A255411(a(n)).

Original entry on oeis.org

0, 1, 2, 5, 6, 13, 14, 23, 24, 49, 50, 77, 54, 85, 86, 119, 120, 241, 242, 365, 246, 373, 374, 503, 264, 409, 410, 557, 414, 565, 566, 719, 720, 1441, 1442, 2165, 1446, 2173, 2174, 2903, 1464, 2209, 2210, 2957, 2214, 2965, 2966, 3719, 1560, 2401, 2402, 3245, 2406, 3253, 3254, 4103, 2424, 3289, 3290, 4157, 3294, 4165, 4166, 5039, 5040, 10081
Offset: 0

Views

Author

Antti Karttunen, Aug 21 2016

Keywords

Crossrefs

Programs

  • Python
    from sympy import factorial as f
    def a007623(n, p=2): return n if n

    0 else '0' for i in x)[::-1] return 0 if n==0 else sum([int(y[i])*f(i + 1) for i in range(len(y))]) def a153880(n): x=(str(a007623(n)) + '0')[::-1] return 0 if n==0 else sum([int(x[i])*f(i + 1) for i in range(len(x))]) def a(n): return 0 if n==0 else a153880(a(n//2)) if n%2==0 else 1 + a255411(a((n - 1)//2)) print([a(n) for n in range(101)]) # Indranil Ghosh, Jun 20 2017

Formula

a(0) = 0, a(2n) = A153880(a(n)), a(2n+1) = 1+A255411(a(n)).
Other identities. For all n >= 0:
a(n) = A225901(A276083(n)).

A276083 a(0) = 0, a(2n) = A255411(a(n)), a(2n+1) = 1+A153880(a(n)).

Original entry on oeis.org

0, 1, 4, 3, 18, 13, 16, 9, 96, 73, 76, 51, 90, 61, 64, 33, 600, 481, 484, 363, 498, 373, 376, 249, 576, 433, 436, 291, 450, 301, 304, 153, 4320, 3601, 3604, 2883, 3618, 2893, 2896, 2169, 3696, 2953, 2956, 2211, 2970, 2221, 2224, 1473, 4200, 3361, 3364, 2523, 3378, 2533, 2536, 1689, 3456, 2593, 2596, 1731, 2610, 1741, 1744, 873, 35280, 30241
Offset: 0

Views

Author

Antti Karttunen, Aug 21 2016

Keywords

Crossrefs

Programs

  • Python
    from sympy import factorial as f
    def a007623(n, p=2): return n if n

    0 else '0' for i in x)[::-1] return 0 if n==0 else sum([int(y[i])*f(i + 1) for i in range(len(y))]) def a153880(n): x=(str(a007623(n)) + '0')[::-1] return 0 if n==0 else sum([int(x[i])*f(i + 1) for i in range(len(x))]) def a(n): return 0 if n==0 else a255411(a(n//2)) if n%2==0 else 1 + a153880(a((n - 1)//2)) print([a(n) for n in range(101)]) # Indranil Ghosh, Jun 20 2017

Formula

a(0) = 0, a(2n) = A255411(a(n)), a(2n+1) = 1+A153880(a(n)).
Other identities. For all n >= 0:
a(n) = A225901(A276082(n)).

A276932 Row 2 of A276953: a(n) = A153880(A273670(n)).

Original entry on oeis.org

2, 8, 12, 14, 26, 32, 36, 38, 50, 56, 60, 62, 72, 74, 78, 80, 84, 86, 122, 128, 132, 134, 146, 152, 156, 158, 170, 176, 180, 182, 192, 194, 198, 200, 204, 206, 242, 248, 252, 254, 266, 272, 276, 278, 290, 296, 300, 302, 312, 314, 318, 320, 324, 326, 362, 368, 372, 374, 386, 392, 396, 398, 410, 416, 420
Offset: 0

Views

Author

Antti Karttunen, Sep 22 2016

Keywords

Comments

Numbers k for which A276949(k) = 2. Starting offset is 0 (with a(0) = 2) to match with the starting offset of A273670.

Crossrefs

Row 2 of A276953, column 2 of A276955, positions of 2's in A276949.
Cf. also A276931 (terms halved).

Formula

a(n) = A153880(A273670(n)).

A273665 a(0) = 0; for n >= 1: if n = A153880(k) for some k, then a(n) = 2*a(k), otherwise, n = A273670(h) for some h, and a(n) = 1 + 2*a(h).

Original entry on oeis.org

0, 1, 2, 3, 5, 7, 4, 11, 6, 15, 9, 23, 10, 13, 14, 31, 19, 47, 21, 27, 29, 63, 39, 95, 8, 43, 22, 55, 59, 127, 12, 79, 30, 191, 17, 87, 18, 45, 46, 111, 119, 255, 25, 159, 61, 383, 35, 175, 20, 37, 26, 91, 93, 223, 28, 239, 62, 511, 51, 319, 38, 123, 94, 767, 71, 351, 41, 75, 53, 183, 187, 447, 42, 57, 54, 479, 125, 1023, 58
Offset: 0

Views

Author

Antti Karttunen, May 30 2016

Keywords

Crossrefs

Inverse: A273666.
Related or similar permutations: A255565, A273667.

Formula

a(0) = 0; for n >= 1: if A257680(A225901(n)) = 0 [i.e., n is one of the terms of A153880], then a(n) = 2*a(A266193(n)), otherwise [when n is one of the terms of A273670], a(n) = 1 + 2*a(A273663(n)).

A276933 Row 3 of A276953: a(n) = A153880(A153880(A273670(n))).

Original entry on oeis.org

6, 30, 48, 54, 126, 150, 168, 174, 246, 270, 288, 294, 360, 366, 384, 390, 408, 414, 726, 750, 768, 774, 846, 870, 888, 894, 966, 990, 1008, 1014, 1080, 1086, 1104, 1110, 1128, 1134, 1446, 1470, 1488, 1494, 1566, 1590, 1608, 1614, 1686, 1710, 1728, 1734, 1800, 1806, 1824, 1830, 1848, 1854, 2166, 2190, 2208, 2214, 2286, 2310
Offset: 0

Views

Author

Antti Karttunen, Sep 23 2016

Keywords

Comments

All terms are multiples of 6. See A276934.

Crossrefs

Row 3 of A276953, column 3 of A276955.
Cf. A153880, A273670, A276932, A276934 (terms divided by six).
Indices of 3's in A276949.

Programs

Formula

a(n) = 6*A276934(n).

A153883 a(n) = A153880(n)/2.

Original entry on oeis.org

0, 1, 3, 4, 6, 7, 12, 13, 15, 16, 18, 19, 24, 25, 27, 28, 30, 31, 36, 37, 39, 40, 42, 43, 60, 61, 63, 64, 66, 67, 72, 73, 75, 76, 78, 79, 84, 85, 87, 88, 90, 91, 96, 97, 99, 100, 102, 103, 120, 121, 123, 124, 126, 127, 132, 133, 135, 136, 138, 139, 144, 145, 147, 148
Offset: 0

Views

Author

Antti Karttunen, Jan 03 2009

Keywords

Crossrefs

Cf. A153880.

Programs

  • Scheme
    ; MIT Scheme
    (define (A153883 n) (let loop ((n n) (z 0) (i 2) (f 1)) (cond ((zero? n) z) (else (loop (floor->exact (/ n i)) (+ (* f (modulo n i)) z) (1+ i) (* f (+ i 1)))))))

A276957 Permutation of natural numbers: a(A153880(n)) = A255411(n), a(A273670(n)) = A256450(n).

Original entry on oeis.org

1, 4, 2, 3, 5, 12, 6, 16, 7, 8, 9, 18, 10, 22, 11, 13, 14, 15, 17, 19, 20, 21, 23, 48, 24, 52, 25, 26, 27, 60, 28, 64, 29, 30, 31, 66, 32, 70, 33, 34, 35, 36, 37, 38, 39, 40, 41, 72, 42, 76, 43, 44, 45, 84, 46, 88, 47, 49, 50, 90, 51, 94, 53, 54, 55, 56, 57, 58, 59, 61, 62, 96, 63, 100, 65, 67, 68, 108, 69, 112, 71, 73
Offset: 1

Views

Author

Antti Karttunen, Sep 22 2016

Keywords

Crossrefs

Inverse: A276958.
For more recursed variants see: A275845, A275847 & A273667.

Programs

Formula

If A276950(n) = 0, then a(n) = A255411(A266193(n)), otherwise a(n) = A256450(A273663(n)).

A276958 Permutation of natural numbers: a(A255411(n)) = A153880(n), a(A256450(n)) = A273670(n).

Original entry on oeis.org

1, 3, 4, 2, 5, 7, 9, 10, 11, 13, 15, 6, 16, 17, 18, 8, 19, 12, 20, 21, 22, 14, 23, 25, 27, 28, 29, 31, 33, 34, 35, 37, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 51, 52, 53, 55, 57, 24, 58, 59, 61, 26, 63, 64, 65, 66, 67, 68, 69, 30, 70, 71, 73, 32, 75, 36, 76, 77, 79, 38, 81, 48, 82, 83, 85, 50, 87, 88, 89, 90, 91, 92, 93, 54
Offset: 1

Views

Author

Antti Karttunen, Sep 22 2016

Keywords

Crossrefs

Inverse: A276957.
For more recursed variants see: A275846, A275848 & A273668.

Programs

Formula

If A257680(n) = 0, then a(n) = A153880(A257684(n)), otherwise a(n) = A273670(A273662(n)).
Previous Showing 11-20 of 51 results. Next