A360188 Primes p such that the six consecutive primes starting at p are congruent to 1,2,4,5,7,8 (mod 9) in that order.

56197, 342037, 464941, 534637, 637327, 651169, 698239, 774919, 823789, 1142083, 1260757, 1382167, 1498789, 1614637, 1625707, 1814599, 1881811, 2213389, 2228509, 2597869, 2602783, 2821141, 2833309, 2980531, 3009043, 3019339, 3056959, 3083869, 3185551, 3204739, 3300139, 3593917, 3837727

Offset

1,1

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..1000

Example

a(1) = 56197 since it is the least prime that is the first of six consecutive primes, {56197, 56207, 56209, 56237, 56239, 56249}, which are congruent to {1, 2, 4, 5, 7, 8} (mod 9).
217 is not a term because [217, 223, 227, 229, 233, 239] (mod 9) = [1, 7, 2, 4, 8, 5].

Mathematica

p = 19; lst = {}; Do[ While[ !PrimeQ[p] || Mod[ NextPrime[p], 9] != 2 || Mod[NextPrime[p, 2], 9] != 4 || Mod[NextPrime[p, 3], 9] != 5 || Mod[NextPrime[p, 4], 9] != 7 || Mod[NextPrime[p, 5], 9] != 8, p += 18]; AppendTo [lst, p]; p += 18, {33}]; lst

Crossrefs

Cf. A038194.

Sequence in context: A230336 A252320 A252020 * A031655 A203964 A198165

Adjacent sequences: A360185 A360186 A360187 * A360189 A360190 A360191

Keyword

nonn

Author

Zak Seidov and Robert G. Wilson v, Jan 29 2023

Status

approved