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%I A083737 #22 Nov 29 2017 11:48:26
%S A083737 1729,2821,6601,8911,15841,29341,41041,46657,52633,63973,75361,101101,
%T A083737 115921,126217,162401,172081,188461,252601,294409,314821,334153,
%U A083737 340561,399001,410041,488881,512461,530881,552721,658801,670033,721801,748657
%N A083737 Pseudoprimes to bases 2, 3 and 5.
%C A083737 a(n) = n-th positive integer k(>1) such that 2^(k-1) == 1 (mod k), 3^(k-1) == 1 (mod k) and 5^(k-1) == 1 (mod k)
%C A083737 See A153580 for numbers k > 1 such that 2^k-2, 3^k-3 and 5^k-5 are all divisible by k but k is not a Carmichael number (A002997).
%C A083737 Note that a(1)=1729 is the Hardy-Ramanujan number. - _Omar E. Pol_, Jan 18 2009
%H A083737 Charles R Greathouse IV, <a href="/A083737/b083737.txt">Table of n, a(n) for n = 1..10000</a> (first 102 from R. J. Mathar)
%H A083737 J. Bernheiden, <a href="http://www.mathe-schule.de/download/pdf/Primzahl/PSP.pdf">Pseudoprimes (Text in German)</a>
%H A083737 F. Richman, <a href="http://math.fau.edu/Richman/carm.htm">Primality testing with Fermat's little theorem</a>
%H A083737 <a href="/https/oeis.org/index/Ps#pseudoprimes">Index entries for sequences related to pseudoprimes</a>
%e A083737 a(1)=1729 since it is the first number such that 2^(k-1) == 1 (mod k), 3^(k-1) == 1 (mod k) and 5^(k-1) == 1 (mod k).
%t A083737 Select[ Range[838200], !PrimeQ[ # ] && PowerMod[2, # - 1, # ] == 1 && PowerMod[3, 1 - 1, # ] == 1 && PowerMod[5, # - 1, # ] == 1 & ]
%o A083737 (PARI) is(n)=!isprime(n)&&Mod(2,n)^(n-1)==1&&Mod(3,n)^(n-1)==1&&Mod(5,n)^(n-1)==1 \\ _Charles R Greathouse IV_, Apr 12 2012
%Y A083737 Proper subset of A052155. Superset of A230722. Cf. A153580, A002997, A001235, A011541.
%K A083737 easy,nonn
%O A083737 1,1
%A A083737 Serhat Sevki Dincer (sevki(AT)ug.bilkent.edu.tr), May 05 2003
%E A083737 Edited by _Robert G. Wilson v_, May 06 2003
%E A083737 Edited by _N. J. A. Sloane_, Jan 14 2009

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