A054203 a(n) is the smallest start of a run of exactly n+1 consecutive primes with n (not necessarily equal) prime differences, each divisible by 6.

23, 47, 251, 1889, 1741, 19471, 118801, 498259, 148531, 406951, 1820111, 2339041, 40727657, 19725473, 73451737, 232301497, 400414121, 1057859471, 489144599, 1444257673, 766319189, 24061965043, 87996684091, 21549657539, 141116164769, 140432294381, 437339303279

Offset

1,1

Comments

This is a "modular arithmetic progression" of successive primes, modulo 6.

Links

Table of n, a(n) for n=1..27.

Index entries for sequences related to primes in arithmetic progressions.

Example

For n = 1: a(1) = 23 is followed by a difference 6 to give 29, a prime.
For n = 5 a(5) = 1741 is followed by differences {6, 6, 6, 18, 6} and results in {1741, 1747, 1753, 1759, 1777, 1783} consecutive prime sequence.
For n = 10: a(10) = 406951 is prime prime is followed by {18, 12, 12, 30, 24, 12, 24, 36, 18, 12} consecutive differences pattern.

Prog

(PARI) list(len) = {my(s = vector(len), v = [], prv = 2, c = 0, i, q, d); forprime(p = 3, , d = p - prv; if(d % 6, if(q > 0, i = #v; if(i > 0 && i <= len && s[i] == 0, s[i] = q; c++)); v = [], if(#v == 0, q = prv); v = concat(v, p)); prv = p; if(c == len, break)); s; } \\ Amiram Eldar, Mar 11 2025

Crossrefs

Cf. A001223, A033451, A052243, A052239.

Sequence in context: A054693 A180945 A052229 * A247673 A216569 A042054

Adjacent sequences: A054200 A054201 A054202 * A054204 A054205 A054206

Keyword

nonn,changed

Author

Labos Elemer, May 17 2000

Extensions

a(11)-a(21) from Sean A. Irvine, Jan 25 2022

a(8) corrected, a(22)-a(27) added, and name clarified by Amiram Eldar, Mar 11 2025

Status

approved