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 A057618 #17 Feb 08 2025 13:58:30
%S A057618 11,181,4831,22501,216401,2229971,3873011,36539311,36539311,196943081,
%T A057618 14293856441,154351758091,154351758091,154351758091,11992377039481,
%U A057618 41947964349971,253931039382791,253931039382791,253931039382791
%N A057618 Initial prime in first sequence of n primes congruent to 1 modulo 5.
%C A057618 a(20) > 4*10^14. - _Giovanni Resta_, Aug 04 2013
%H A057618 J. K. Andersen, <a href="http://primerecords.dk/congruent-primes.htm">Consecutive Congruent Primes</a>.
%H A057618 Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_016.htm">Puzzle 16 - Consecutive primes and ending digit</a>, The prime puzzles & problems connection.
%e A057618 a(6) = 2229971 because this number is the first in a sequence of 6 consecutive primes all of the form 5n + 1.
%t A057618 NextPrime[ n_Integer ] := Module[ {k = n + 1}, While[ ! PrimeQ[ k ], k++ ]; Return[ k ] ]; PrevPrime[ n_Integer ] := Module[ {k = n - 1}, While[ ! PrimeQ[ k ], k-- ]; Return[ k ] ]; p = 0; Do[ a = Table[ -1, {n} ]; k = Max[ 1, p ]; While[ Union[ a ] != {1}, k = NextPrime[ k ]; a = Take[ AppendTo[ a, Mod[ k, 5 ] ], -n ] ]; p = NestList[ PrevPrime, k, n ]; Print[ p[ [ -2 ] ] ]; p = p[ [ -1 ] ], {n, 1, 10} ]
%Y A057618 Cf. A054681.
%K A057618 nonn
%O A057618 1,1
%A A057618 _Robert G. Wilson v_, Oct 09 2000
%E A057618 More terms from _Jens Kruse Andersen_, Jun 03 2006
%E A057618 a(15)-a(19) from _Giovanni Resta_, Aug 04 2013