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

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

Author

Leroy Quet, Sep 28 2009

Keywords

• base
• nonn

Links

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

Crossrefs

Cf. A007088, A001737.

Cf. A165819, A165821, A165822, A294977.

Programs

Mathematica

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 *)

Formula

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

Extensions

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