A392862 a(n) = A143293(n)+14 mod prime(n+1), where A143293 gives the partial sums of primorials.

1, 2, 3, 4, 10, 12, 14, 17, 6, 20, 25, 23, 18, 12, 18, 40, 42, 9, 18, 68, 37, 51, 9, 62, 25, 31, 46, 82, 99, 48, 92, 26, 134, 42, 82, 38, 90, 130, 31, 69, 54, 17, 105, 125, 146, 147, 209, 89, 193, 58, 225, 122, 17, 77, 35, 42, 99, 36, 222, 251, 23, 180, 95, 197, 219, 222, 208, 73, 163, 113, 173, 59, 175, 108, 370

Offset

0,2

Comments

The first zeros occur at 11980, 35050.

The terms of this sequence occurs as the digits in the primorial base expansion of the terms of A392864 (when read from right to left), from the term A392864(8) up to the term A392864(11980-1), after which, at n=11980 the pattern changes because of the first zero occurring in this sequence, entailing that A392615(11980) = 32 > 14 for the first time.

Links

Antti Karttunen, Table of n, a(n) for n = 0..12000

Index entries for sequences related to primorial numbers.

Mathematica

Mod[Accumulate[FoldList[Times, 1, Most[#]]] + 14, #] & [Prime[Range[100]]] (* Paolo Xausa, Jan 26 2026 *)

Prog

(PARI) A392862(n) = { my(q=prime(n+1), P=Mod(1, q), s=P+Mod(14, q)); forprime(p=2, q-1, s+=P*=p); lift(s); }; \\ After Charles R Greathouse IV's Sep 22 2022 program for A357270

Crossrefs

Cf. A143293, A357270, A392615, A392864.

Sequence in context: A023725 A250051 A076079 * A229593 A196007 A134170

Adjacent sequences: A392859 A392860 A392861 * A392863 A392864 A392865

Keyword

nonn

Author

Antti Karttunen, Jan 26 2026

Status

approved