A249113 Take n and successively add 1, 2, ..., a(n) until reaching a prime for the third time.

4, 5, 16, 5, 11, 13, 8, 6, 19, 6, 12, 13, 7, 9, 28, 5, 11, 13, 12, 17, 19, 6, 11, 25, 8, 6, 28, 5, 20, 37, 7, 14, 19, 10, 11, 34, 8, 6, 40, 6, 20, 25, 8, 9, 31, 6, 11, 25, 19, 21, 19, 6, 12, 25, 16, 9, 28, 5, 20, 22, 7, 14, 40, 9, 11, 34, 19, 6, 52, 17, 12

Offset: 1

Author

Gil Broussard, Oct 21 2014

Keywords

• easy
• nonn

Comments

Conjecturally (Hardy & Littlewood conjecture F), a(n) exists for all n. - Charles R Greathouse IV, Oct 21 2014

Examples

			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).
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A085415, A249112.

Programs

Mathematica

Table[k = 0; Do[k++; While[! PrimeQ[n + Total@ Range@ k], k++], {x, 3}]; k, {n, 71}] (* Michael De Vlieger, Jan 03 2016 *)

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

Formula

n+A000217(k) is prime for k=a(n) and exactly two smaller positive values. - M. F. Hasler, Oct 21 2014