A392860 a(n) = 1 + Sum_{i=1..n} (p_i - 2)*(p_i#/p_i), where p_i stands for the i-th prime, and p_i# = A002110(i), the i-th primorial number.

1, 1, 3, 21, 171, 2061, 27471, 477921, 9156591, 212850081, 6236357571, 193857461241, 7213474615791, 296622261873381, 12770883066488991, 601495142991640341, 31960874055004702251, 1889542907254837251861, 115332403566353382956991, 7739077191927806496869541, 549963264216466233352526751, 40163762203212092462039019441

Offset

0,3

Comments

Term a(n) for n > 0 can be formed by taking the n-th primorial, A002110(n), subtracting one to get the n-th Kummer number A057588(n), which always has a primorial base expansion with n maximal digits allowed in those digit positions in the primorial base (see A049345), then subtracting one from each of those primorial base digits, except from the least significant (rightmost) 1, which is kept intact.

For n > 0, lim inf_{n->oo} a(n+1)/a(n) = A000040(1+n)-1. See A392861. - Amiram Eldar and Antti Karttunen, Jan 25 2026

Links

Table of n, a(n) for n=0..21.

Index entries for sequences related to primorial base.

Index entries for sequences related to primorial numbers.

Formula

For n > 0, a(n) = 1 + A328842(A057588(n)).

For n > 0, a(n) = A143293(n) - 2*A143293(n-1) = A002110(n) - A143293(n-1).

Prog

(PARI)
A002110(n) = prod(i=1, n, prime(i));
A392860(n) = (1+sum(i=1, n, (prime(i)-2)*A002110(i-1)));

Crossrefs

Cf. A002110, A049345, A057588, A328842, A143293, A392861.

Cf. also A392607.

Sequence in context: A206178 A233861 A206397 * A247480 A365136 A228923

Adjacent sequences: A392857 A392858 A392859 * A392861 A392862 A392863

Keyword

nonn,base,easy

Author

Antti Karttunen, Jan 25 2026

Status

approved