A339866 Primes that are simultaneously the sums of 11, 13, and 15 consecutive primes.

8472193, 14084311, 16569827, 28358851, 33546551, 45993127, 91174081, 123593753, 186861293, 205286087, 224010023, 227568853, 310359607, 335497667, 423104119, 454320901, 482749429, 492404317, 558048187, 560997023, 566428813, 700508971, 707060359, 715731761, 735276379

Offset

1,1

Comments

Intersection of A127340, A127341, A161612.

The first case with 17 consecutive primes is a(219) = 8410721789. Are there more such terms?

a(10) = 205286087 is the sum of k consecutive primes not only for k = 11, 13, and 15, but also for k=1 (i.e., a(10) is a prime), k=9, and k=233. - Jon E. Schoenfield, Apr 24 2021

Links

Table of n, a(n) for n=1..25.

Example

Sum_{k=61746..61756} prime(k) = Sum_{k=52937..52949} prime(k) = Sum_{k=46425..46439} prime(k) = 8472193, so 8472193 is a term. - Jon E. Schoenfield, Apr 24 2021

Mathematica

Module[{nn=4*10^6, prs, p11, p13, p15}, prs=Prime[Range[nn]]; p11=Total/@Partition[prs, 11, 1]; p13=Total/@Partition[prs, 13, 1]; p15=Total/@ Partition[ prs, 15, 1]; Select[Intersection[ p11, p13, p15], PrimeQ]] (* Harvey P. Dale, Aug 14 2023 *)

Crossrefs

Cf. A127340, A127341, A161612, A213914.

Sequence in context: A049362 A251119 A205179 * A251173 A203824 A081639

Adjacent sequences: A339863 A339864 A339865 * A339867 A339868 A339869

Keyword

nonn

Author

Zak Seidov, Apr 24 2021

Status

approved