A122259 Primes p such that p - 1 is not 3-smooth.

11, 23, 29, 31, 41, 43, 47, 53, 59, 61, 67, 71, 79, 83, 89, 101, 103, 107, 113, 127, 131, 137, 139, 149, 151, 157, 167, 173, 179, 181, 191, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347

Offset: 1

Author

Reinhard Zumkeller, Aug 29 2006

Keywords

• nonn
• easy

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Pierpont Prime

Crossrefs

Cf. A005109, A006530, A122257.

Programs

Mathematica

smooth3Q[n_] := n == 2^IntegerExponent[n, 2]*3^IntegerExponent[n, 3];
Select[Prime[Range[100]], !smooth3Q[#-1]&] (* Jean-François Alcover, Oct 17 2021 *)

PARI

is(n)=my(q=n-1); q>>=valuation(q,2); q/=3^valuation(q,3); q>1 && isprime(n) \\ Charles R Greathouse IV, Oct 29 2018

Formula

A122257(a(n)) = 0;

A006530(a(n) - 1) > 3.

a(n) ~ n log n. - Charles R Greathouse IV, Oct 29 2018