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A260524
Pseudoprimes to bases 2, 3, 5 and 7 that are congruent to 5 (modulo 6) but are not Carmichael numbers (A002997).
1
468950021, 493108481, 659846021, 5936122901, 8144063621, 11408333333, 12601267541, 14252656133, 18074903681, 27223783841, 30633711701, 31093792133, 31797754721, 61426533761, 65085388961, 86610942881, 91945013333, 92380393121, 102538073177
OFFSET
1,1
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
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
PROG
(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
CROSSREFS
Cf. A153581.
Sequence in context: A349747 A323653 A246548 * A091677 A147717 A127888
KEYWORD
nonn
EXTENSIONS
a(9)-a(19) from Charles R Greathouse IV, Jul 29 2015
STATUS
approved