OFFSET
1,1
COMMENTS
Take the counting numbers and continue adding 1, 2, ..., a(n) until reaching a second prime.
Conjecturally (Hardy & Littlewood conjecture F), a(n) exists for all n. - Charles R Greathouse IV, Oct 21 2014
It appears that the minimum value reached by a(n) is 2, and this occurs for n= 2, 4, 10, 16, 28, 40, 58, 70, ... Is this A144834? - Michel Marcus, Oct 26 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 one smaller positive value. - M. F. Hasler, Oct 21 2014
EXAMPLE
a(3)=7 because 3+1+2+3+4+5+6+7=31 and one partial sum is prime.
a(4)=2 because 4+1=5 and 4+1+2=7.
MATHEMATICA
Table[k = 0; Do[k++; While[! PrimeQ[n + Total@ Range@ k], k++], {x, 2}]; k, {n, 77}] (* Michael De Vlieger, Jan 03 2016 *)
PROG
(PARI) a(n)=my(k, s=2); while(s, if(isprime(n+=k++), s--)); k \\ Charles R Greathouse IV, Oct 21 2014
(PARI) a(n, s=2)=my(k); until(isprime(n+=k++)&&!s--, ); k \\ allows one to get A249113(n) as a(n, 3). - M. F. Hasler, Oct 21 2014
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Gil Broussard, Oct 21 2014
STATUS
approved