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 A249113 Take n and successively add 1, 2, ..., a(n) until reaching a prime for the third time. 3
 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 (list; graph; refs; listen; history; text; internal format)
 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 A244643 A085768 Adjacent sequences: A249110 A249111 A249112 * A249114 A249115 A249116 KEYWORD easy,nonn AUTHOR Gil Broussard, Oct 21 2014 STATUS approved

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Last modified January 31 18:02 EST 2023. Contains 359980 sequences. (Running on oeis4.)