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A054656
Number of primes <= n which do not appear in any partitions of n into distinct primes.
0
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
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
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
KEYWORD
nonn
AUTHOR
Henry Bottomley, Apr 17 2000
EXTENSIONS
a(17) corrected and more terms from Sean A. Irvine, Feb 15 2022
STATUS
approved