A145257 a(n) is the smallest integer > n that is non-coprime to n and has the same number of 0's in its binary representation as n has.

6, 15, 10, 30, 14, 63, 18, 12, 12, 55, 21, 247, 30, 63, 34, 85, 20, 57, 24, 28, 26, 253, 38, 45, 28, 30, 46, 1015, 55, 1023, 66, 36, 36, 42, 40, 185, 42, 45, 48, 205, 44, 215, 50, 51, 54, 14335, 69, 56, 52, 54, 56, 159, 57, 95, 77, 60, 60, 767, 87, 4087, 126, 255, 130, 80

Offset: 2

Author

Leroy Quet, Oct 05 2008

Keywords

• base
• nonn

Links

• Rémy Sigrist, Table of n, a(n) for n = 2..10000
• Rémy Sigrist, PARI program for A145257

Crossrefs

Cf. A023416 (number of 0's in binary expansion of n).

Cf. A140977, A145254, A145255, A145256.

Programs

Magma

a:=[]; for n in [2..70] do k:=n+1; while Gcd(n,k) eq 1 or  Multiplicity(Intseq(n,2),0) ne  Multiplicity(Intseq(k,2),0) do k:=k+1; end while; Append(~a,k); end for; a; // Marius A. Burtea, Feb 06 2020

Mathematica

a[n_] := Block[{},i = n + 1; While[GCD[i, n] == 1 || Not[DigitCount[n, 2, 0] == DigitCount[i, 2, 0]], i++ ]; i]; Table[a[n], {n, 2, 100}] (* Stefan Steinerberger, Oct 17 2008 *)
sncp[n_]:=Module[{k=n+1},While[CoprimeQ[k,n]||DigitCount[k,2,0]!=DigitCount[ n,2,0],k++];k]; Array[sncp,70,2] (* Harvey P. Dale, Aug 11 2024 *)

PARI

\\ See Links section.

PARI

a(n) = {my(m = n+1, nb = #binary(n) - hammingweight(n)); while (!((gcd(m, n) > 1) && (nb == #binary(m) - hammingweight(m))), m++); m;} \\ Michel Marcus, Feb 06 2020

Extensions

More terms from Stefan Steinerberger, Oct 17 2008

a(58)-a(64) from Ray Chandler, Jun 20 2009