A307610 Number of partitions of prime(n) into consecutive primes.

1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 1, 2, 2, 1, 2, 2, 1, 1, 3, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 3, 3, 2, 3, 1, 1, 2, 1, 1, 3, 1, 2, 2, 2, 1, 3, 1, 1, 1, 5, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 1, 3, 1, 1, 2, 2, 1, 3, 2, 2, 2, 1, 2, 1, 2, 2, 3, 2, 2, 1, 1, 2

Offset

1,3

Comments

a(n) - 1 = number of partitions of prime(n) into two or more consecutive primes. - Ray Chandler, Sep 26 2023

Links

Ray Chandler, Table of n, a(n) for n = 1..1000

Formula

a(n) = [x^prime(n)] Sum_{i>=1} Sum_{j>=i} Product_{k=i..j} x^prime(k).

a(n) = A054845(A000040(n)).

Example

prime(13) = 41 = 2 + 3 + 5 + 7 + 11 + 13 = 11 + 13 + 17, so a(13) = 3.

Crossrefs

Cf. A000040, A034707, A054845, A056768, A070215, A084143.

Sequence in context: A345985 A103765 A344772 * A125029 A339839 A062893

Adjacent sequences: A307607 A307608 A307609 * A307611 A307612 A307613

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 18 2019

Status

approved