A083736 Pseudoprimes to bases 2,5 and 7.
561, 29341, 46657, 75361, 115921, 162401, 252601, 294409, 314821, 334153, 340561, 399001, 410041, 488881, 512461, 530881, 552721, 656601, 658801, 710533, 721801, 852841, 1024651, 1141141, 1152271, 1168513, 1193221, 1461241, 1569457, 1615681
Offset: 1
Examples
a(1)=561 since it is the first number such that 2^(k-1) = 1 (mod k), 5^(k-1) = 1 (mod k) and 7^(k-1) = 1 (mod k).
Links
- Amiram Eldar, Table of n, a(n) for n = 1..8691 (terms 1..81 from R. J. Mathar)
- F. Richman, Primality testing with Fermat's little theorem
Crossrefs
Intersection of A083732 and A005938. Intersection of A083733 and A005936. - R. J. Mathar, Apr 05 2011
Programs
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Mathematica
Select[Range[1, 10^5, 2], CompositeQ[#] && PowerMod[2, #-1,#] == PowerMod[5, #-1,#] == PowerMod[7, #-1,#] == 1&] (* Amiram Eldar, Jun 29 2019 *)
Formula
a(n) = n-th positive integer k(>1) such that 2^(k-1) = 1 (mod k), 5^(k-1) = 1 (mod k) and 7^(k-1) = 1 (mod k).