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A066868
a(n) is the least k such that n + Sum_{i=1..k} A005385(i) is prime; or 0 if none exists.
0
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, 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, 1, 2, 1, 10, 5, 2, 7, 10, 1, 6, 7, 2, 1, 8, 3, 4, 7, 26, 1
OFFSET
1,1
COMMENTS
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.
EXAMPLE
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.
PROG
(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
CROSSREFS
Sequence in context: A126450 A235608 A112333 * A193900 A319373 A143172
KEYWORD
nonn,less
AUTHOR
Joseph L. Pe, Jan 21 2002
EXTENSIONS
Offset changed to 1 by Jinyuan Wang, Jul 30 2020
STATUS
approved