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A260524
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Pseudoprimes to bases 2, 3, 5 and 7 that are congruent to 5 (modulo 6) but are not Carmichael numbers (A002997).
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1
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468950021, 493108481, 659846021, 5936122901, 8144063621, 11408333333, 12601267541, 14252656133, 18074903681, 27223783841, 30633711701, 31093792133, 31797754721, 61426533761, 65085388961, 86610942881, 91945013333, 92380393121, 102538073177
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OFFSET
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1,1
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LINKS
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MATHEMATICA
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fQ[n_] := !PrimeQ[n] && PowerMod[2, n - 1, n] == 1 &&
> PowerMod[3, n - 1, n] == 1 && PowerMod[5, n - 1, n] == 1 && PowerMod[7, n - 1, n] == 1 && Mod[n, CarmichaelLambda[n]] != 1; k = 1; lst = {}; While[k < 25000000001, If[ fQ@ k, AppendTo[lst, k]; Print@ k]; k += 6]; lst
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PROG
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(PARI) Korselt(n)=my(f=factor(n)); for(i=1, #f[, 1], if(f[i, 2]>1||(n-1)%(f[i, 1]-1), return(0))); 1
is(n)=n%6==5 && Mod(2, n)^n==2 && Mod(3, n)^n==3 && Mod(5, n)^(n-1)==1 && Mod(7, n)^(n-1)==1 && !isprime(n) && !Korselt(n) \\ Charles R Greathouse IV, Jul 29 2015
(Perl) use ntheory ":all"; foroddcomposites { say if $_%6 == 5 && is_pseudoprime($_, 2, 3, 5, 7) && $_ % carmichael_lambda($_) != 1; } 1e9; # Dana Jacobsen, Sep 07 2015
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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