A194946 Odd non-Carmichael numbers with increasing numbers of bases to which they are pseudoprimes.

9, 15, 45, 65, 91, 231, 325, 341, 481, 703, 1541, 1891, 2701, 5461, 6533, 8321, 11041, 12403, 18721, 30889, 38503, 49141, 68101, 79003, 88561, 88831, 104653, 137149, 146611, 176149, 188191, 218791, 226801, 269011, 286903, 385003, 493697, 497503, 563473

Offset: 1

Author

Charles R Greathouse IV, Sep 13 2011

Keywords

• nonn

Comments

A141768 is the analog using the Rabin-Miller test rather than the Fermat test. The infinitude of that sequence implies that this sequence is likewise infinite.

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..659
• Index entries for sequences related to pseudoprimes

Crossrefs

Cf. A195327 (number of bases).

Cf. A141768.

Programs

PARI

bases(n)=my(f=factor(n)[,1]);n--;prod(i=1,#f,gcd(f[i]-1,n))
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
r=0;p=5;forprime(q=7,1e7,forstep(n=p+2,q-2,2,if(bases(n)>r&&!Korselt(n), r=bases(n);print1(n", ")));p=q) \\ Charles R Greathouse IV, Sep 14 2011