A260524 Pseudoprimes to bases 2, 3, 5 and 7 that are congruent to 5 (modulo 6) but are not Carmichael numbers (A002997).

468950021, 493108481, 659846021, 5936122901, 8144063621, 11408333333, 12601267541, 14252656133, 18074903681, 27223783841, 30633711701, 31093792133, 31797754721, 61426533761, 65085388961, 86610942881, 91945013333, 92380393121, 102538073177

Offset: 1

Author

Ray Chandler, Artur Jasinski and Robert G. Wilson v, Jul 28 2015

Keywords

• nonn

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A153581.

Programs

Mathematica

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

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

Extensions

a(9)-a(19) from Charles R Greathouse IV, Jul 29 2015