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

1,1

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

Cf. A085415, A249112.

Sequence in context: A323627 A289742 A340850 * A166590 A368739 A244643

Adjacent sequences: A249110 A249111 A249112 * A249114 A249115 A249116

Keyword

easy,nonn

Author

Gil Broussard, Oct 21 2014

Status

approved