A392616 a(n) is the least k>=1 such that A143293(n)+k is prime, where A143293 give the partial sums of primorial numbers.

1, 2, 2, 2, 2, 20, 14, 14, 20, 32, 14, 98, 58, 44, 118, 22, 74, 44, 140, 32, 40, 32, 14, 14, 58, 112, 118, 14, 58, 98, 98, 410, 62, 32, 152, 172, 362, 22, 64, 148, 190, 58, 172, 944, 32, 112, 970, 40, 322, 14, 394, 74, 212, 128, 760, 124, 14, 152, 128, 194, 298, 40, 218, 344, 344, 172, 302, 124, 638, 64, 74, 62

Offset

0,2

Comments

Question: When is a(n) = A392615(n)? At least on n = 1, 2, 3, 4, 10, 22, 23, 27, 49, 56, ...

Links

Table of n, a(n) for n=0..71.

Formula

a(n) >= A392615(n).

Prog

(PARI)
A143293(n) = { if(n==0, return(1)); my(P=1, s=1); forprime(p=2, prime(n), s+=P*=p); s; };
A392616(n) = { my(b=A143293(n)); for(k=1, oo, if(isprime(b+k), return(k))); };

Crossrefs

Cf. A143293, A392615.

Cf. also A005235, A281318.

Sequence in context: A100687 A067096 A259704 * A249779 A167394 A029627

Adjacent sequences: A392613 A392614 A392615 * A392617 A392618 A392619

Keyword

nonn

Author

Antti Karttunen, Jan 24 2026

Status

approved