A127340 -id:A127340 - cp's OEIS frontend

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

Zak Seidov, Apr 24 2021

nonn

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

			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

Cf. A127340, A127341, A161612, A213914.

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 *)

A341338 a(n) is the smallest prime that is simultaneously the sum of 2n-1, 2n+1 and 2n+3 consecutive primes.

Original entry on oeis.org

83, 311, 55813, 437357, 1219789, 8472193, 9496853, 6484103, 2166953, 37296143, 12671599, 13432571, 14968909, 145616561, 732092831, 220872569, 1381099933, 93482633, 4142423, 87030017, 3193060007, 736535783, 6390999871, 280886077, 464341303, 268231657, 686836817, 9000046663

Offset: 1

Zak Seidov, Apr 25 2021

nonn

			For n = 1: 83 = 23 + 29 + 31 = 11 + 13 + 17 + 19 + 23, and 83 is the smallest prime that is the sum of 1, 3 and 5 consecutive primes, so a(1) = 83.

Cf. A034962, A034965, A082246, A082251, A127340, A127341, A161612.

Array[(k=1;
While[(i=Select[Intersection@@((Total/@Subsequences[Prime@Range@Prime[k++],{#}])&/@{2#-1,2#+1,2#+3}),PrimeQ])=={}];First@i)&,4] (* Giorgos Kalogeropoulos, Apr 26 2021 *)

cp's OEIS Frontend

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

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