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 A083737 Pseudoprimes to bases 2, 3 and 5. 11
 1729, 2821, 6601, 8911, 15841, 29341, 41041, 46657, 52633, 63973, 75361, 101101, 115921, 126217, 162401, 172081, 188461, 252601, 294409, 314821, 334153, 340561, 399001, 410041, 488881, 512461, 530881, 552721, 658801, 670033, 721801, 748657 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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) 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). Note that a(1)=1729 is the Hardy-Ramanujan number. - Omar E. Pol, Jan 18 2009 LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 102 from R. J. Mathar) J. Bernheiden, Pseudoprimes (Text in German) F. Richman, Primality testing with Fermat's little theorem EXAMPLE 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). MATHEMATICA Select[ Range[838200], !PrimeQ[ # ] && PowerMod[2, # - 1, # ] == 1 && PowerMod[3, 1 - 1, # ] == 1 && PowerMod[5, # - 1, # ] == 1 & ] PROG (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 CROSSREFS Proper subset of A052155. Superset of A230722. Cf. A153580, A002997, A001235, A011541. Sequence in context: A300949 A198775 A154729 * A182208 A324316 A182207 Adjacent sequences:  A083734 A083735 A083736 * A083738 A083739 A083740 KEYWORD easy,nonn AUTHOR Serhat Sevki Dincer (sevki(AT)ug.bilkent.edu.tr), May 05 2003 EXTENSIONS Edited by Robert G. Wilson v, May 06 2003 Edited by N. J. A. Sloane, Jan 14 2009 STATUS approved

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Last modified December 1 06:09 EST 2020. Contains 338833 sequences. (Running on oeis4.)