A294977 -id:A294977 - cp's OEIS frontend

A165819 a(n) = the smallest positive integer that, when written in binary, contains both binary n and binary 2n-1 as substrings.

1, 6, 11, 28, 37, 22, 29, 120, 137, 83, 43, 92, 205, 59, 61, 496, 529, 291, 595, 167, 169, 86, 183, 376, 793, 410, 437, 220, 925, 123, 125, 2016, 2081, 1091, 2211, 583, 293, 1227, 2471, 2536, 2601, 339, 171, 2796, 729, 366, 751, 1520, 3121, 1586, 1637, 1652

Offset: 1

Leroy Quet, Sep 28 2009

If a(n) in binary was instead to contain binary n and binary 2n+1 as substrings, then a(n) would = 2n+1 for all n.

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Cf. A165820, A165821, A165822, A294977.

a(n) = A294977(n, 2*n-1). - Rémy Sigrist, Mar 03 2018

More terms from Carl R. White, Oct 06 2009

A165820 a(n) = the smallest positive integer that, when written in binary, contains both binary n and binary n^2 as substrings.

Original entry on oeis.org

1, 4, 19, 16, 89, 100, 113, 64, 593, 1380, 377, 400, 425, 452, 481, 256, 4385, 1298, 723, 10640, 5561, 11748, 8471, 18456, 1649, 1700, 729, 1808, 1865, 1924, 1985, 1024, 33857, 9250, 36041, 75024, 5477, 11558, 40433, 83520, 1681, 87780, 22329, 92048

Offset: 1

Leroy Quet, Sep 28 2009

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Cf. A007088, A001737.

Cf. A165819, A165821, A165822, A294977.

f[n_] := Block[{k = 1, is = IntegerString[n, 2], iss = IntegerString[n^2, 2]}, While[ StringPosition[ IntegerString[k, 2], is] == {} || StringPosition[ IntegerString[k, 2], iss] == {}, k++ ]; k]; Array[f, 44] (* Robert G. Wilson v, Oct 02 2009 *)

a(n) = A294977(n, n^2). - Rémy Sigrist, Mar 03 2018

a(7)-a(44) from Robert G. Wilson v, Oct 02 2009

A165821 a(n) = the smallest positive integer that, when written in binary, contains both binary n and the binary representation of the n-th prime as substrings.

Original entry on oeis.org

2, 6, 11, 28, 11, 13, 71, 152, 151, 58, 95, 101, 105, 174, 47, 848, 571, 978, 1075, 327, 1173, 719, 1335, 1432, 1561, 1626, 827, 860, 237, 241, 127, 131, 4233, 139, 4501, 1175, 4765, 2467, 167, 1384, 5299, 362, 703, 705, 1581, 1479, 3027, 3568, 227, 229

Offset: 1

Leroy Quet, Sep 28 2009

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Cf. A000040, A165819, A165820, A165822, A294977.

a(n) = A294977(n, A000040(n)). - Rémy Sigrist, Mar 03 2018

More terms from Carl R. White, Oct 06 2009

A165822 a(n) = the smallest positive integer that, when written in binary, contains both binary n and the binary representation of the n-th Fibonacci number as substrings.

Original entry on oeis.org

1, 2, 6, 12, 5, 24, 29, 168, 137, 442, 89, 400, 233, 377, 7778, 15792, 1597, 18968, 66899, 6765, 10946, 181551, 28657, 1483800, 206097, 121393, 458562, 317811, 514229, 3977768, 21540319, 2178309, 56393249, 72811751, 9227465, 618910128

Offset: 1

Leroy Quet, Sep 28 2009

Rémy Sigrist, Table of n, a(n) for n = 1..1000

Cf. A000045, A165819, A165820, A165821, A294977.

a(n) = A294977(n, A000045(n)). - Rémy Sigrist, Mar 03 2018

More terms from Carl R. White, Oct 06 2009

cp's OEIS Frontend

A165819 a(n) = the smallest positive integer that, when written in binary, contains both binary n and binary 2n-1 as substrings.

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A165820 a(n) = the smallest positive integer that, when written in binary, contains both binary n and binary n^2 as substrings.

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A165821 a(n) = the smallest positive integer that, when written in binary, contains both binary n and the binary representation of the n-th prime as substrings.

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A165822 a(n) = the smallest positive integer that, when written in binary, contains both binary n and the binary representation of the n-th Fibonacci number as substrings.

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