A122257 Characteristic function of Pierpont primes (A005109).

0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Author

Reinhard Zumkeller, Aug 29 2006

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Eric Weisstein's World of Mathematics, Pierpont Prime.
• Index entries for characteristic functions.

Crossrefs

Cf. A005109, A010051, A065333, A122258 (partial sums).

Programs

Mathematica

smooth3Q[n_] := n == 2^IntegerExponent[n, 2]*3^IntegerExponent[n, 3];
a[n_] := Boole[PrimeQ[n] && smooth3Q[n - 1]];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Oct 16 2021 *)

PARI

is3smooth(n) = my(m = n >> valuation(n, 2)); m == 3^valuation(m, 3);
a(n) = isprime(n) && is3smooth(n-1); \\ Amiram Eldar, May 14 2025

Scheme

(define (A122257 n) (if (= 1 n) 0 (if (= 1 (A065333 (- n 1))) (A010051 n) 0)))
(define (A065333 n) (if (= 1 (A038502 (A000265 n))) 1 0))
;; Antti Karttunen, Dec 07 2017

Formula

a(n) = A010051(n) * A065333(n-1).

a(n) = if (n is prime) and (n-1 is 3-smooth) then 1 else 0.

a(n) = if n=1 then 0 else A122258(n) - A122258(n-1);

a(A122259(n)) = 0, a(A005109(n)) = 1.