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

1,1

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

Prog

(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

Crossrefs

Cf. A195327 (number of bases).

Cf. A141768.

Sequence in context: A193579 A274757 A146789 * A020172 A020174 A020315

Adjacent sequences: A194943 A194944 A194945 * A194947 A194948 A194949

Keyword

nonn

Author

Charles R Greathouse IV, Sep 13 2011

Status

approved