A083739 Pseudoprimes to bases 2, 3, 5 and 7.

29341, 46657, 75361, 115921, 162401, 252601, 294409, 314821, 334153, 340561, 399001, 410041, 488881, 512461, 530881, 552721, 658801, 721801, 852841, 1024651, 1152271, 1193221, 1461241, 1569457, 1615681, 1857241, 1909001, 2100901

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.

Index entries for sequences related to pseudoprimes.

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).

A005938 INTERSECT A083737. - R. J. Mathar, Feb 07 2008

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

Cf. A001567, A005935, A005936, A005938.

Proper subset of A083737.

Sequence in context: A250940 A186566 A083740 * A329538 A182133 A182416

Adjacent sequences: A083736 A083737 A083738 * A083740 A083741 A083742

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