A107745 Smallest prime factor of 6*n-1.

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

Author

Zak Seidov, May 23 2005

Keywords

• nonn
• easy

Comments

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

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