A290170 Primes prime(k) such that prime(k-1) + prime(k+1) = prime(k-2) + prime(k+2) = prime(k-3) + prime(k+3).

59, 67, 73, 367, 379, 569, 587, 631, 757, 967, 1033, 1039, 1439, 1523, 1613, 2383, 2459, 2699, 3571, 4027, 4139, 4253, 4259, 4451, 4889, 6113, 6269, 6299, 6983, 7001, 7019, 7687, 9181, 9203, 9811, 9833, 10079, 11261, 11923, 12569, 12703, 13883, 14549, 15787

Offset

1,1

Comments

Take groups of seven consecutive primes and sum terms {1st + 7th, 2nd + 6th, 3rd + 5th}. If these sums coincide, the middle term, i.e., the 4th one, is in the sequence.

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..10000

Example

3, 5, 7, [11], 13, 17, 19; Sums: {3 + 19, 5 + 17, 7 + 13} = {22, 22, 20}. Sums do not coincide, so 11 is not in the sequence.
43, 47, 53, [59], 61, 67, 71; Sums: {43 + 71, 47 + 67, 53 + 61} = {114, 114, 114}. Sums coincide, so 59 is in the sequence.

Maple

ss := []:
for n from 0 to 5000 do
  pp := [seq(ithprime(n+i), i = 1 .. 7)];
  if pp[1]+pp[7] = pp[2]+pp[6] = pp[3]+pp[5] then
    ss := [op(ss), pp[4]];
  end if;
end do:
ss := ss

Mathematica

p = {2, 3, 5, 7, 11, 13, 17}; lst = {}; While[ p[[1]] < 25000, If[ p[[1]] + p[[7]] == p[[2]] + p[[6]] == p[[3]] + p[[5]], AppendTo[lst, p[[4]] ]]; p = Join[Rest@ p, {NextPrime@p[[-1]]}]]; lst (* Robert G. Wilson v, Jul 23 2017 *)

Crossrefs

Cf. A227064.

Sequence in context: A172056 A032648 A235808 * A033237 A139894 A048988

Adjacent sequences: A290167 A290168 A290169 * A290171 A290172 A290173

Keyword

nonn

Author

César Eliud Lozada, Jul 23 2017

Status

approved