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
Keywords
Examples
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.
Programs
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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
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
Comments