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A054656

Number of primes <= n which do not appear in any partitions of n into distinct primes.

0, 0, 0, 1, 2, 0, 3, 1, 2, 2, 0, 4, 1, 3, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 2, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 2, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 2, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 2, 0, 1, 1, 0, 0, 1, 1, 1, 0

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OFFSET

0,5

COMMENTS

Conjecture: if n >= 23 then a(n)=2 if both (n-6) and (n-4) are prime, a(n)=1 if one of (n-6), (n-4) or (n-1) is prime, a(n)=0 otherwise

LINKS

Table of n, a(n) for n=0..86.

EXAMPLE

a(17)=2 since 17=2+3+5+7 and there are no other partitions of 17 into distinct primes, so the primes 2,3,5,7 and occur at least once but 11 and 13 do not. - Sean A. Irvine, Feb 15 2022

a(22)=1 since 22=2+7+13=2+3+17=5+17=3+19, so the primes 2,3,5,7,13,17 and 19 appear at least once but 11 does not.

CROSSREFS

Cf. A000586.

Sequence in context: A293813 A218585 A279507 * A080096 A322978 A294142

Adjacent sequences: A054653 A054654 A054655 * A054657 A054658 A054659

KEYWORD

nonn

AUTHOR

Henry Bottomley, Apr 17 2000

EXTENSIONS

a(17) corrected and more terms from Sean A. Irvine, Feb 15 2022

STATUS

approved