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

1,1

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.

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.

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 *)

Prog

(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
(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

Crossrefs

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

Sequence in context: A286484 A118247 A286487 * A332219 A227625 A373497

Adjacent sequences: A122254 A122255 A122256 * A122258 A122259 A122260

Keyword

nonn

Author

Reinhard Zumkeller, Aug 29 2006

Status

approved