login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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. [From Omar E. Pol, Jan 18 2009]

LINKS

R. J. Mathar, Table of n, a(n) for n = 1..102

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^(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: A033181 A198775 A154729 * A182208 A182207 A138129

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified June 25 00:41 EDT 2017. Contains 288708 sequences.