

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
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OFFSET

1,1


COMMENTS

a(n) = nth positive integer k(>1) such that 2^(k1) == 1 (mod k), 3^(k1) == 1 (mod k) and 5^(k1) == 1 (mod k)
See A153580 for numbers k > 1 such that 2^k2, 3^k3 and 5^k5 are all divisible by k but k is not a Carmichael number (A002997).
Note that a(1)=1729 is the HardyRamanujan 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
Index entries for sequences related to pseudoprimes


EXAMPLE

a(1)=1729 since it is the first number such that 2^(k1) == 1 (mod k), 3^(k1) == 1 (mod k) and 5^(k1) == 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)^(n1)==1&&Mod(3, n)^(n1)==1&&Mod(5, n)^(n1)==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



