A382249 a(n) is the smallest starting prime of a sequence of exactly n consecutive primes that are alternately of the form 6*k+1 and 6*k-1 or vice versa.

23, 19, 17, 13, 11, 7, 5, 97, 89, 877, 863, 859, 857, 853, 839, 829, 827, 823, 821, 811, 809, 3954889, 15186331, 15186323, 15186319, 77011331, 77011303, 77011289, 288413249, 288413233, 288413219, 288413173, 288413159, 62585146739, 114058236679, 143014298851, 143014298831, 143014298809

Offset

1,1

Links

Table of n, a(n) for n=1..38.

Example

a(1) = 23, because 23 and 29 are 2 consecutive primes such that 23 = 6*4 - 1, while 29 = 6*5 - 1. Additionally, no smaller prime possesses this property.
a(2) = 19, because 19, 23 and 29 are 3 consecutive primes such that 19 = 6*3 + 1 and 23 = 6*4 - 1, while 29 = 6*5 - 1. Additionally, no smaller prime possesses this property.
Table of consecutive primes
  1 [23] = 6*[4] + [-1];
  2 [19, 23] = 6*[3, 4] + [1, -1];
  3 [17, 19, 23] = 6*[3, 3, 4] + [-1, 1, -1];
  4 [13, 17, 19, 23] = 6*[2, 3, 3, 4] + [1, -1, 1, -1];
  5 [11, 13, 17, 19, 23] = 6*[2, 2, 3, 3, 4] + [-1, 1, -1, 1, -1];

Crossrefs

Cf. A057620, A057622.

Sequence in context: A204598 A160436 A105818 * A085450 A077146 A077576

Adjacent sequences: A382246 A382247 A382248 * A382250 A382251 A382252

Keyword

nonn

Author

Jean-Marc Rebert, Mar 19 2025

Status

approved