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.

Showing 1-3 of 3 results.

A092601 Number of numbers from 1 to n whose binary representation is contained in that of n!.

Original entry on oeis.org

1, 2, 3, 4, 4, 6, 7, 8, 8, 9, 9, 9, 12, 14, 14, 15, 16, 17, 18, 19, 20, 21, 23, 23, 24, 26, 26, 28, 28, 30, 27, 28, 33, 34, 35, 35, 34, 37, 39, 38, 40, 42, 43, 43, 44, 45, 43, 46, 48, 48, 51, 51, 53, 53, 53, 55, 56, 58, 55, 59, 61, 62, 63, 64, 64, 66, 65, 68, 68, 70, 70, 71, 73
Offset: 1

Views

Author

Reinhard Zumkeller, Apr 08 2004

Keywords

Comments

Sequence is not monotonic.

Examples

			n = 5: 5! = 1*2*3*4*5 = 120 = '1111000': 1 = '1', 2 = '10', 3 = '11' and 4 = '100' are contained, but not 5 = '101', therefore a(5) = 4.

Links

Crossrefs

Cf. A000142, A007088, A036603, A093710, A093711.

Programs

  • Mathematica
    f[n_] := ToString[ FromDigits[ IntegerDigits[n, 2]]]; g[n_] := Block[{c = 0, k = 1, s = f[n! ]}, While[k <= n, If[ StringPosition[ s, f[k]] != {}, c++ ]; k++ ]; c]; Table[ g[n], {n, 75}] (* Robert G. Wilson v, Apr 21 2004 *)

Formula

a(A093710(n)) = n, a(A093711(n)) < n.

A093711 Numbers k such that in their binary representation not all numbers from 1 to k are contained in k!.

Original entry on oeis.org

5, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 27, 29, 31, 32, 36, 37, 38, 40, 41, 44, 45, 46, 47, 48, 49, 50, 52, 54, 55, 56, 57, 59, 60, 65, 67, 69, 71, 72, 74, 75, 76, 78, 79, 81, 82, 84, 85, 86, 87, 88, 89, 90, 91, 92, 95, 96, 97, 98, 99, 100, 101, 102
Offset: 1

Views

Author

Reinhard Zumkeller, Apr 11 2004

Keywords

Links

Crossrefs

Complement of A093710.
A093685 \ {0} is a subsequence.
Cf. A000142, A007088, A036603, A092601.

Formula

A092601(a(n)) < a(n).

A092762 Least number whose binary representation is not contained in that of n!.

Original entry on oeis.org

2, 3, 4, 5, 5, 7, 10, 10, 7, 9, 7, 5, 13, 15, 15, 15, 17, 17, 15, 17, 18, 17, 29, 21, 17, 28, 20, 31, 21, 36, 15, 15, 35, 42, 41, 35, 33, 22, 45, 22, 36, 46, 50, 41, 37, 33, 21, 40, 38, 31, 66, 33, 60, 45, 51, 42, 42, 60, 35, 38, 63, 65, 75, 75, 39, 71, 36, 75, 67, 74, 67, 68, 78
Offset: 1

Views

Author

Reinhard Zumkeller, Apr 13 2004

Keywords

Comments

a(A093710(n)) > n, a(A093711(n)) <= n.
Sum_{n=1..3000} a(n) = 4179226. The average value of a(n)/n -> 0.93+ and except for some initial terms, < 212, 0.90 < a(n)/n < 0.95. But there is graphical evidence that this value may increase. - Robert G. Wilson v, Apr 21 2004
a(n) = n only for 5, 13, 15, 17, 513, 517, 1041, 1538, 2138, n <= 2500. a(n) = n+1 for n=1, 2, 3, 4, 6, 14, 134, 137, 155, 169, 216, 313, 530, 1035 & 2402. - Robert G. Wilson v, Apr 21 2004
a(n) >= 3n/2 for n=1, 2, 334, 335, 2693 & 2739. - Robert G. Wilson v, Apr 21 2004
a(n) <= n/2 for n=12, 31, 32, 47, 122, 142, 152, 188, 303, 378, 443, 548, 598, 1319, 1354, 1420, 2127, 2137, 2223, 2230, 2368, 2433, 2571. - Robert G. Wilson v, Apr 21 2004

Examples

			a(7)=10 because 7! = 1001110110000_b and 1_b, 10_b, 11_b, 100_b, 101_b, 110_b, 111_b, 1000_b & 1001_b are substrings, but 10_d = 1010_b is not a substring. - _Robert G. Wilson v_, Apr 21 2004

Crossrefs

Cf. A036603, A007088, A000142, A092601.

Programs

  • Mathematica
    f[n_] := ToString[ FromDigits[ IntegerDigits[n, 2]]]; g[n_] := g[n] = Block[{k = 1, s = f[n! ]}, While[ StringPosition[ s, f[k]] != {}, k++ ]; k]; Table[ g[n], {n, 75}] (* Robert G. Wilson v, Apr 21 2004 *)

Extensions

Edited by N. J. A. Sloane, Sep 15 2008 at the suggestion of R. J. Mathar
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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