A309383 a(n) is the smallest b > 1 such that when c is equal to any of the first n composites the congruence b^(c-1) == 1 (mod c) is satisfied, i.e., smallest b larger than 1 such that any member of the set of smallest n composites is a base-b Fermat pseudoprime.

5, 13, 25, 73, 361, 361, 2521, 2521, 5041, 5041, 5041, 5041, 55441, 55441, 277201, 3603601, 10810801, 10810801, 10810801, 21621601, 21621601, 367567201, 367567201, 367567201

Offset

1,1

Links

Table of n, a(n) for n=1..24.

Example

For n = 4: The four smallest composites are 4, 6, 8, 9 and for those four values of c the congruence b^(c-1) == 1 (mod c) is satisfied with b = 73. Since 73 is the smallest such value of b > 1, a(4) = 73.

Prog

(PARI) composites(n) = my(v=[]); forcomposite(c=1, , v=concat(v, [c]); if(#v >= n, return(v)))
a(n) = my(cp=composites(n)); for(b=2, oo, for(k=1, #cp, if(Mod(b, cp[k])^(cp[k]-1)!=1, break, if(k==#cp, return(b)))))

Crossrefs

Cf. A242742, A256236.

Sequence in context: A107466 A098480 A018394 * A147451 A173979 A190446

Adjacent sequences: A309380 A309381 A309382 * A309384 A309385 A309386

Keyword

nonn,more

Author

Felix Fröhlich, Jul 27 2019

Status

approved