This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A054203 #18 Mar 11 2025 04:39:03
%S A054203 23,47,251,1889,1741,19471,118801,498259,148531,406951,1820111,
%T A054203 2339041,40727657,19725473,73451737,232301497,400414121,1057859471,
%U A054203 489144599,1444257673,766319189,24061965043,87996684091,21549657539,141116164769,140432294381,437339303279
%N 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.
%C A054203 This is a "modular arithmetic progression" of successive primes, modulo 6.
%H A054203 <a href="/index/Pri#primes_AP">Index entries for sequences related to primes in arithmetic progressions</a>.
%e A054203 For n = 1: a(1) = 23 is followed by a difference 6 to give 29, a prime.
%e A054203 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.
%e A054203 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.
%o A054203 (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
%Y A054203 Cf. A001223, A033451, A052243, A052239.
%K A054203 nonn
%O A054203 1,1
%A A054203 _Labos Elemer_, May 17 2000
%E A054203 a(11)-a(21) from _Sean A. Irvine_, Jan 25 2022
%E A054203 a(8) corrected, a(22)-a(27) added, and name clarified by _Amiram Eldar_, Mar 11 2025