A382700 First member of the least set of 5 consecutive primes such that the sum of each pair of consecutive primes in this set is a multiple of n.

2, 3, 5, 47, 3593, 5, 10487, 523, 38377, 3593, 1796671, 409, 947423, 10487, 60383, 62501, 18164651, 38377, 15095579, 32633, 3272567, 1796671, 116863451, 67819, 65835479, 947423, 7005239, 1165217, 1154953243, 60383, 800037461, 7442557, 15442121, 18164651, 771405431

Offset: 1

Author

Paolo P. Lava, Apr 04 2025

Keywords

• nonn

Examples

			a(4) = 47. The least 5 consecutive primes are 47, 53, 59, 61, 67:
  47 + 53 = 100 and 100/4 = 25;
  53 + 59 = 112 and 112/4 = 28;
  59 + 61 = 120 and 120/4 = 30;
  61 + 67 = 128 and 128/4 = 32.
a(27) = 7005239. The least 5 consecutive primes are 7005239, 7005277, 7005293, 7005331, 7005347:
  7005239 + 7005277 = 14010516 and 14010516/27 = 518908;
  7005277 + 7005293 = 14010570 and 14010570/27 = 518910;
  7005293 + 7005331 = 14010624 and 14010624/27 = 518912;
  7005331 + 7005347 = 14010678 and 14010678/27 = 518914.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..50
• Carlos Rivera, Conjecture 92. For any integer m there is at least one set of consecutive primes..., The Prime Puzzles and Problems Connection.

Crossrefs

Cf. A254862 (2 consecutive), A382698 (3 consecutive), A382699 (4 consecutive).