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A083739
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Pseudoprimes to bases 2, 3, 5 and 7.
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5
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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
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OFFSET
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1,1
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LINKS
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FORMULA
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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).
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EXAMPLE
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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).
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MAPLE
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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
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MATHEMATICA
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Select[ Range[2113920], !PrimeQ[ # ] && PowerMod[2, # - 1, # ] == 1 && PowerMod[3, 1 - 1, # ] == 1 && PowerMod[5, # - 1, # ] == 1 && PowerMod[7, 1 - 1, # ] == 1 & ]
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Serhat Sevki Dincer (sevki(AT)ug.bilkent.edu.tr), May 05 2003
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EXTENSIONS
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STATUS
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approved
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