A309383 - OEIS

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.

%I #14 Jul 28 2019 10:26:26

%S 5,13,25,73,361,361,2521,2521,5041,5041,5041,5041,55441,55441,277201,

%T 3603601,10810801,10810801,10810801,21621601,21621601,367567201,

%U 367567201,367567201

%N 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.

%e 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.

%o (PARI) composites(n) = my(v=[]); forcomposite(c=1, , v=concat(v, [c]); if(#v >= n, return(v)))

%o 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)))))

%Y Cf. A242742, A256236.

%K nonn,more

%O 1,1

%A _Felix Fröhlich_, Jul 27 2019