A145256 a(n) = the smallest integer > n that is non-coprime to n and has the same number of 1's in its binary representation as n has.

4, 6, 8, 10, 9, 14, 16, 12, 12, 22, 18, 26, 21, 27, 32, 34, 20, 38, 24, 28, 26, 46, 33, 35, 28, 30, 35, 58, 39, 62, 64, 36, 36, 42, 40, 74, 42, 45, 48, 82, 44, 86, 50, 51, 54, 94, 66, 56, 52, 54, 56, 106, 57, 110, 70, 60, 60, 118, 75, 122, 93, 111, 128, 80, 68, 134, 72, 81, 74

Offset: 2

Author

Leroy Quet, Oct 05 2008

Keywords

• base
• nonn

Comments

a(n) <= 2n since 2n is trivially a multiple of n and multiplying a number by 2 adds a 0 in base 2. - Stefan Steinerberger, Oct 17 2008

Links

• Rémy Sigrist, Table of n, a(n) for n = 2..65536

Crossrefs

Cf. A145254, A145255, A145257.

Programs

Mathematica

a[n_] := Block[{}, i = n + 1; While[GCD[i, n] == 1 || Not[DigitCount[n, 2, 1] == DigitCount[i, 2, 1]], i++ ]; i]; Table[a[n], {n, 2, 100}] (* Stefan Steinerberger, Oct 17 2008 *)

PARI

a(n) = for (m=n+1, oo, if (gcd(m,n)>1 && hammingweight(m)==hammingweight(n), return (m))) \\ Rémy Sigrist, Feb 06 2020

Extensions

Edited and corrected by Stefan Steinerberger, Oct 17 2008