1,1

R. J. Mathar, Table of n, a(n) for n = 1..114

J. Bernheiden, Pseudoprimes (Text in German)

F. Richman, Primality testing with Fermat's little theorem

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)

A005938 INTERSECT A083737. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 07 2008

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)

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 (mathar(AT)strw.leidenuniv.nl), Feb 07 2008

Select[ Range[2113920], !PrimeQ[ # ] && PowerMod[2, # - 1, # ] == 1 && PowerMod[3, 1 - 1, # ] == 1 && PowerMod[5, # - 1, # ] == 1 && PowerMod[7, 1 - 1, # ] == 1 & ]

Proper subset of A083737.

Adjacent sequences: A083736 A083737 A083738 this_sequence A083740 A083741 A083742

Sequence in context: A028462 A058652 A083740 this_sequence A022200 A056747 A106771

easy,nonn

Serhat Sevki Dincer (sevki(AT)ug.bilkent.edu.tr), May 05 2003

Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), May 06 2003