OFFSET
1,1
COMMENTS
Conjecturally (Hardy & Littlewood conjecture F), a(n) exists for all n. - Charles R Greathouse IV, Oct 21 2014
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
FORMULA
n+A000217(k) is prime for k=a(n) and exactly two smaller positive values. - M. F. Hasler, Oct 21 2014
EXAMPLE
a(1)=4 because 1+1+2+3+4=11 and exactly two partial sums are prime (2,7).
a(2)=5 because 2+1+2+3+4+5=17 and exactly two partial sums are prime (3,5).
MATHEMATICA
Table[k = 0; Do[k++; While[! PrimeQ[n + Total@ Range@ k], k++], {x, 3}]; k, {n, 71}] (* Michael De Vlieger, Jan 03 2016 *)
PROG
(PARI) a(n)=my(k, s=3); while(s, if(isprime(n+=k++), s--)); k \\ Charles R Greathouse IV, Oct 21 2014
(PARI) a(n, s=3)=my(k); until(isprime(n+=k++)&&!s--, ); k \\ allows one to get A249112(n) as a(n, 2). - M. F. Hasler, Oct 21 2014
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Gil Broussard, Oct 21 2014
STATUS
approved