OFFSET
1,1
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..7469 (terms below 10^12; terms 1..114 from R. J. Mathar)
Jens Bernheiden, Pseudoprimes (in German).
Fred Richman, Primality testing with Fermat's little theorem.
FORMULA
a(n) = n-th positive integer k(>1) such that 2^(k-1) = 1 (mod k), 3^(k-1) = 1 (mod k), 5^(k-1) = 1 (mod k) and 7^(k-1) = 1 (mod k).
EXAMPLE
a(1)=29341 since it is the first number such that 2^(k-1) = 1 (mod k), 3^(k-1) = 1 (mod k), 5^(k-1) = 1 (mod k) and 7^(k-1) = 1 (mod k).
MAPLE
a001567 := [] : f := fopen("b001567.txt", READ) : bfil := readline(f) : while StringTools[WordCount](bfil) > 0 do if StringTools[FirstFromLeft]("#", bfil ) <> 0 then ; else bfil := sscanf(bfil, "%d %d") ; a001567 := [op(a001567), op(2, bfil) ] ; fi ; bfil := readline(f) ; od: fclose(f) : isPsp := proc(n, b) if n>3 and not isprime(n) and b^(n-1) mod n = 1 then true; else false; fi; end: isA001567 := proc(n) isPsp(n, 2) ; end: isA005935 := proc(n) isPsp(n, 3) ; end: isA005936 := proc(n) isPsp(n, 5) ; end: isA005938 := proc(n) isPsp(n, 7) ; end: isA083739 := proc(n) if isA001567(n) and isA005935(n) and isA005936(n) and isA005938(n) then true ; else false ; fi ; end: n := 1: for psp2 from 1 do i := op(psp2, a001567) ; if isA083739(i) then printf("%d %d ", n, i) ; n :=n+1 ; fi ; od: # R. J. Mathar, Feb 07 2008
MATHEMATICA
Select[ Range[2113920], !PrimeQ[ # ] && PowerMod[2, # - 1, # ] == 1 && PowerMod[3, 1 - 1, # ] == 1 && PowerMod[5, # - 1, # ] == 1 && PowerMod[7, 1 - 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&&Mod(7, n)^(n-1)==1 \\ Charles R Greathouse IV, Apr 12 2012
CROSSREFS
KEYWORD
nonn
AUTHOR
Serhat Sevki Dincer (sevki(AT)ug.bilkent.edu.tr), May 05 2003
EXTENSIONS
Edited by Robert G. Wilson v, May 06 2003
STATUS
approved