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%I #7 Aug 01 2020 11:38:03
%S 2,1,10,5,2,1,2,1,12,5,2,1,4,1,4,5,2,1,2,3,4,7,12,1,2,1,4,7,2,3,2,1,4,
%T 5,2,1,4,1,6,17,2,1,4,3,6,5,2,1,2,3,4,11,12,1,2,1,4,5,2,3,2,1,4,5,14,
%U 1,2,1,10,5,2,7,10,1,6,7,2,1,8,3,4,7,26,1
%N a(n) is the least k such that n + Sum_{i=1..k} A005385(i) is prime; or 0 if none exists.
%C Conjecture: a(n) is nonzero for all n, so every n can be represented as the difference between a prime and a partial sum of the safe primes series. See A066753 for a similar conjecture.
%e 4 + (5 + 7 + 11 + 23 + 47) = 97, a prime and 5 consecutive safe primes, starting from the first safe prime 5, are needed to achieve this. Hence a(4) = 5.
%o (PARI) a(n) = my(p=3, s=n); for(k=1, oo, until(isprime((p-1)/2), p=nextprime(p+1)); if(isprime(s+=p), return(k))); \\ _Jinyuan Wang_, Jul 30 2020
%Y Cf. A005385, A066753.
%K nonn,less
%O 1,1
%A _Joseph L. Pe_, Jan 21 2002
%E Offset changed to 1 by _Jinyuan Wang_, Jul 30 2020
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