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 A005936 M3712 #51 Jul 08 2025 16:38:37
%S A005936 4,124,217,561,781,1541,1729,1891,2821,4123,5461,5611,5662,5731,6601,
%T A005936 7449,7813,8029,8911,9881,11041,11476,12801,13021,13333,13981,14981,
%U A005936 15751,15841,16297,17767,21361,22791,23653,24211,25327,25351,29341,29539
%N A005936 Pseudoprimes to base 5.
%C A005936 According to Karsten Meyer, 4 should be excluded, following the strict definition in Crandall and Pomerance. - May 16 2006
%C A005936 Theorem: If both numbers q and (2q - 1) are primes (q is in the sequence A005382) then n = q*(2q - 1) is a pseudoprime to base 5 (n is in the sequence) if and only if q is of the form 10k + 1. 1891, 88831, 146611, 218791, 721801, ... are such terms. This sequence is a subsequence of A122782. - _Farideh Firoozbakht_, Sep 14 2006
%C A005936 Composite numbers n such that 5^(n-1) == 1 (mod n).
%D A005936 R. Crandall and C. Pomerance, "Prime Numbers - A Computational Perspective", Second Edition, Springer Verlag 2005, ISBN 0-387-25282-7 Page 132 (Theorem 3.4.2. and Algorithm 3.4.3)
%D A005936 J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 124, p. 43, Ellipses, Paris 2008.
%D A005936 R. K. Guy, Unsolved Problems in Number Theory, A12.
%D A005936 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A005936 R. J. Mathar, T. D. Noe and Hiroaki Yamanouchi, <a href="/A005936/b005936.txt">Table of n, a(n) for n = 1..92893</a> (terms a(1)-a(776) from R. J. Mathar, a(777)-a(1000) from T. D. Noe)
%H A005936 J. Bernheiden, <a href="http://www.mathe-schule.de/download/pdf/Primzahl/PSP.pdf">Pseudoprimes (Text in German)</a>
%H A005936 C. Pomerance & N. J. A. Sloane, <a href="/A001567/a001567_4.pdf">Correspondence, 1991</a>
%H A005936 F. Richman, <a href="http://math.fau.edu/Richman/carm.htm">Primality testing with Fermat's little theorem</a>
%H A005936 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FermatPseudoprime.html">Fermat Pseudoprime</a>
%H A005936 <a href="/index/Ps#pseudoprimes">Index entries for sequences related to pseudoprimes</a>
%t A005936 base = 5; t = {}; n = 1; While[Length[t] < 100, n++; If[! PrimeQ[n] && PowerMod[base, n-1, n] == 1, AppendTo[t, n]]]; t (* _T. D. Noe_, Feb 21 2012 *)
%t A005936 Select[Range[30000],CompositeQ[#]&&PowerMod[5,#-1,#]==1&] (* _Harvey P. Dale_, Jul 21 2023 *)
%Y A005936 Pseudoprimes to other bases: A001567 (2), A005935 (3), A005937 (6), A005938 (7), A005939 (10).
%Y A005936 Cf. A005382, A122782.
%K A005936 nonn
%O A005936 1,1
%A A005936 _N. J. A. Sloane_
%E A005936 More terms from _David W. Wilson_, Aug 15 1996