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
Keywords
Examples
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];