A083740 Pseudoprimes to bases 3,5 and 7.
29341, 46657, 75361, 88831, 115921, 146611, 162401, 252601, 294409, 314821, 334153, 340561, 399001, 410041, 488881, 512461, 530881, 552721, 658801, 721801, 852841, 954271, 1024651, 1152271, 1193221, 1314631, 1461241, 1569457, 1615681
Offset: 1
Examples
a(1)=29341 since it is the first number such that 3^(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..8702 (terms 1..77 from R. J. Mathar)
- F. Richman, Primality testing with Fermat's little theorem
Programs
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Mathematica
Select[Range[1, 10^5, 2], CompositeQ[#] && PowerMod[3, #-1, #] == PowerMod[5, #-1, #] == PowerMod[7, #-1, #] == 1&]
Formula
a(n) = n-th positive integer k(>1) such that 3^(k-1) = 1 (mod k), 5^(k-1) = 1 (mod k) and 7^(k-1) = 1 (mod k).
Intersection of A083734 and A005938. Intersection of A083735 and A005936. - R. J. Mathar, Apr 05 2011