A260524 - OEIS

%I #16 Sep 07 2015 14:43:05

%S 468950021,493108481,659846021,5936122901,8144063621,11408333333,

%T 12601267541,14252656133,18074903681,27223783841,30633711701,

%U 31093792133,31797754721,61426533761,65085388961,86610942881,91945013333,92380393121,102538073177

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

%H Charles R Greathouse IV, <a href="/A260524/b260524.txt">Table of n, a(n) for n = 1..10000</a>

%t fQ[n_] := !PrimeQ[n] && PowerMod[2, n - 1, n] == 1 &&

%t > 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

%o (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

%o 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

%o (Perl) use ntheory ":all"; foroddcomposites { say if $_%6 == 5 && is_pseudoprime($_,2,3,5,7) && $_ % carmichael_lambda($_) != 1; } 1e9; # _Dana Jacobsen_, Sep 07 2015

%Y Cf. A153581.

%K nonn

%O 1,1

%A _Ray Chandler_, _Artur Jasinski_ and _Robert G. Wilson v_, Jul 28 2015

%E a(9)-a(19) from _Charles R Greathouse IV_, Jul 29 2015