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.

A107745 Smallest prime factor of 6*n-1.

Original entry on oeis.org

5, 11, 17, 23, 29, 5, 41, 47, 53, 59, 5, 71, 7, 83, 89, 5, 101, 107, 113, 7, 5, 131, 137, 11, 149, 5, 7, 167, 173, 179, 5, 191, 197, 7, 11, 5, 13, 227, 233, 239, 5, 251, 257, 263, 269, 5, 281, 7, 293, 13, 5, 311, 317, 17, 7, 5, 11, 347, 353, 359, 5, 7, 13, 383, 389, 5, 401, 11
Offset: 1

Views

Author

Zak Seidov, May 23 2005

Keywords

Comments

If 6*n-1 is prime, a(n) = 6*n-1.

Links

Crossrefs

Cf. A020639, A016969, A111863.
Cf. A107744 (smallest prime factor of 6*n+1), A107746 (values of k such that A107744(k) > A107745(k)), A107747 (values of k such that A107744(k) < A107745(k)).

Programs

  • Magma
    [Min(PrimeFactors(6*n-1)):n in[1..68]]; // Jason Kimberley, Oct 28 2015
  • Mathematica
    a[n_]:= FactorInteger[6*n - 1][[1, 1]]; Array[a, 100]
  • PARI
    vector(100, n, vecmin(factor(6*n-1)[, 1])) \\ Altug Alkan, Oct 23 2015

Formula

a(n) = A020639(6n-1). - R. J. Mathar, Jan 23 2007
5 <= a(n) <= 6n - 1; both bounds are sharp. - Charles R Greathouse IV, Sep 02 2024

Extensions

Comments corrected and (at the suggestion of Michel Marcus) moved to Crossrefs by Jason Kimberley, Oct 23 2015

A107744 Smallest prime factor of 6*n+1.

Original entry on oeis.org

7, 13, 19, 5, 31, 37, 43, 7, 5, 61, 67, 73, 79, 5, 7, 97, 103, 109, 5, 11, 127, 7, 139, 5, 151, 157, 163, 13, 5, 181, 11, 193, 199, 5, 211, 7, 223, 229, 5, 241, 13, 11, 7, 5, 271, 277, 283, 17, 5, 7, 307, 313, 11, 5, 331, 337, 7, 349, 5, 19, 367, 373, 379, 5, 17, 397, 13, 409
Offset: 1

Views

Author

Zak Seidov, May 23 2005

Keywords

Comments

If 6*n+1 is prime, a(n) = 6*n+1.

Links

Crossrefs

Cf. A016921, A020639.
Cf. A107745 (smallest prime factor of 6*n-1), A107746 (values of k such that A107744(k) > A107745(k)), A107747 (values of k such that A107744(k) < A107745(k)).

Programs

  • Magma
    [Min(PrimeFactors(6*n+1)):n in[1..68]]; // Jason Kimberley, Oct 28 2015
  • Mathematica
    A107744[n_]:= FactorInteger[6 n + 1][[1, 1]]
  • PARI
    vector(100, n, vecmin(factor(6*n+1)[, 1])) \\ Altug Alkan, Oct 23 2015

Formula

a(n) = A020639(A016921(n)). - Amiram Eldar, Nov 03 2024

Extensions

Comments corrected and (at the suggestion of Michel Marcus) moved to Crossrefs by Jason Kimberley, Oct 23 2015

A107746 Numbers k such that the least prime factor of 6*k+1 > the least prime factor of 6*k-1, A107744(k) > A107745(k).

Original entry on oeis.org

1, 2, 3, 5, 6, 7, 10, 11, 12, 13, 16, 17, 18, 20, 21, 23, 25, 26, 27, 30, 31, 32, 33, 35, 36, 37, 38, 40, 41, 45, 46, 47, 48, 51, 52, 55, 56, 58, 61, 62, 63, 66, 68, 70, 71, 72, 73, 76, 77, 81, 83, 86, 87, 88, 90, 91, 95, 96, 97, 100, 101, 102, 103, 105, 106, 107, 110, 111
Offset: 1

Views

Author

Zak Seidov, May 23 2005

Keywords

Comments

Complement of A107747 in the positive integers.
Contains A016861. - Robert Israel, Oct 23 2015

Links

Crossrefs

Cf. A016861, A107744, A107745, A107747.

Programs

  • Maple
    lpf:= n -> min(numtheory:-factorset(n)):
select(n -> lpf(6*n+1) > lpf(6*n-1), [$1..1000]); # Robert Israel, Oct 23 2015
  • Mathematica
    Select[Range@ 111, FactorInteger[6 # + 1][[1, 1]] > FactorInteger[6 # - 1][[1, 1]] &] (* Michael De Vlieger, Oct 23 2015 *)
  • PARI
    isok(n) = vecmin(factor(6*n+1)[,1]) > vecmin(factor(6*n-1)[,1]); \\ Michel Marcus, Feb 04 2014

Extensions

Comments corrected and (at the suggestion of Michel Marcus) moved to Crossrefs by Jason Kimberley, Oct 23 2015
Showing 1-3 of 3 results.

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