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A307610
Number of partitions of prime(n) into consecutive primes.
6
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
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 18 2019
STATUS
approved