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%I #8 Feb 15 2022 17:11:22
%S 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,
%T 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,
%U 1,0,0,1,1,1,1,1,0,2,0,1,1,0,0,1,1,1,0
%N Number of primes <= n which do not appear in any partitions of n into distinct primes.
%C 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
%e 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
%e 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.
%Y Cf. A000586.
%K nonn
%O 0,5
%A _Henry Bottomley_, Apr 17 2000
%E a(17) corrected and more terms from _Sean A. Irvine_, Feb 15 2022