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A083740 Pseudoprimes to bases 3,5 and 7. 1

%I #17 Jun 29 2019 10:32:03

%S 29341,46657,75361,88831,115921,146611,162401,252601,294409,314821,

%T 334153,340561,399001,410041,488881,512461,530881,552721,658801,

%U 721801,852841,954271,1024651,1152271,1193221,1314631,1461241,1569457,1615681

%N Pseudoprimes to bases 3,5 and 7.

%H Amiram Eldar, <a href="/A083740/b083740.txt">Table of n, a(n) for n = 1..8702</a> (terms 1..77 from R. J. Mathar)

%H F. Richman, <a href="http://math.fau.edu/Richman/carm.htm">Primality testing with Fermat's little theorem</a>

%F 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).

%F Intersection of A083734 and A005938. Intersection of A083735 and A005936. - _R. J. Mathar_, Apr 05 2011

%e 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).

%t Select[Range[1, 10^5, 2], CompositeQ[#] && PowerMod[3, #-1, #] == PowerMod[5, #-1, #] == PowerMod[7, #-1, #] == 1&]

%Y Cf. A005935, A005936, A005938, A083734, A083735.

%K easy,nonn

%O 1,1

%A Serhat Sevki Dincer (sevki(AT)ug.bilkent.edu.tr), May 05 2003

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