A122258 Number of Pierpont primes <= n.

0, 1, 2, 2, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10

Offset: 1

Author

Reinhard Zumkeller, Aug 29 2006

Keywords

• nonn

Links

• Eric Weisstein's World of Mathematics, Pierpont Prime.

Crossrefs

Partial sums of A122257.

Cf. A000720, A005109, A071521.

Programs

Mathematica

smooth3Q[n_] := Times @@ ({2, 3}^IntegerExponent[n, {2, 3}]) == n; s[n_] := Boole[PrimeQ[n] && smooth3Q[n-1]]; Accumulate[Table[s[n], {n, 1, 100}]] (* Amiram Eldar, May 14 2025 *)

PARI

is3smooth(n) = my(m = n >> valuation(n, 2)); m == 3^valuation(m, 3);
f(n) = isprime(n) && is3smooth(n-1);
list(lim) = {my(s = 0); for(n = 1, lim, s += f(n); print1(s, ", "));} \\ Amiram Eldar, May 14 2025

Formula

a(n) <= A000720(n).

a(n) <= A071521(n).