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.

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.

Original entry on oeis.org

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

Views

Author

Leroy Quet, Oct 05 2008

Keywords

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

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

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.

Original entry on oeis.org

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

Views

Author

Leroy Quet, Oct 05 2008

Keywords

Links

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

A145255 a(n) = the smallest positive integer that is non-coprime to n and has the same number of 0's in its binary representation as n has.

Original entry on oeis.org

2, 3, 4, 5, 2, 7, 8, 9, 4, 11, 4, 13, 2, 3, 16, 17, 8, 19, 8, 9, 4, 23, 8, 10, 4, 6, 4, 29, 2, 31, 32, 33, 16, 20, 16, 37, 8, 9, 16, 41, 8, 43, 8, 9, 4, 47, 16, 35, 8, 9, 8, 53, 4, 5, 8, 9, 4, 59, 4, 61, 2, 3, 64, 65, 32, 67, 32, 33, 16, 71, 32, 73, 16, 18, 16, 35, 8, 79, 32, 33, 16, 83, 16
Offset: 2

Views

Author

Leroy Quet, Oct 05 2008

Keywords

Links

Crossrefs

Cf. A145254, A145256, A145257.

Programs

  • Mathematica
    Table[Function[k, SelectFirst[Range[2, n], And[! CoprimeQ[#, n], DigitCount[#, 2, 0] == k] &]]@ DigitCount[n, 2, 0], {n, 2, 84}] (* Michael De Vlieger, Oct 26 2017 *)

Extensions

Extended by Ray Chandler, Nov 03 2008
Showing 1-3 of 3 results.

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

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