A382285 Initial members of prime octuplets (p, p+4, p+12, p+24, p+28, p+40, p+48, p+52), where all primes are consecutive primes.

241639, 44533249, 120833809, 245843149, 480454939, 547838359, 945331939, 1272712579, 1318911019, 1334157859, 1413122899, 1801178629, 1977960949, 2708995099, 3073533559, 3234255499, 3359304829, 3485412349, 3836960419, 4202567899, 4311168259, 4984840999, 5044981129

Offset

1,1

Comments

All gaps are twice the length of respective gaps in the prime octuplet form, (p, p+2, p+6, p+12, p+14, p+20, p+24, p+26). See A022012 for initial members of that pattern.

Terms are congruent to 19 (mod 30).

It is conjectured that there is an infinite number of primes for every admissible k-tuple.

Links

Table of n, a(n) for n=1..23.

Eric Weisstein's World of Mathematics, k-Tuple Conjecture.

Prog

(PARI) list(lim) = {my(d0 = [4, 8, 12, 4, 12, 8, 4], s = vecsum(d0), d = vector(7, i, prime(i+1) - prime(i)), prv = 19); forprime(p = 23, lim, d = concat(vecextract(d, "^1"), p - prv); if(d == d0, print1(p - s, ", ")); prv = p); } \\ Amiram Eldar, Mar 21 2025

Crossrefs

Cf. A022012.

Sequence in context: A249194 A281887 A127881 * A387290 A134857 A251007

Adjacent sequences: A382282 A382283 A382284 * A382286 A382287 A382288

Keyword

nonn

Author

Federico Salas, Mar 20 2025

Extensions

More terms from Amiram Eldar, Mar 21 2025

Status

approved