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

Author

Felix Fröhlich, Jul 27 2019

Keywords

• nonn
• more

Examples

			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.
		

Crossrefs

Cf. A242742, A256236.

Programs

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)))))