A344827 a(n) is the smallest b > 1 such that prime(n), prime(n+1) and prime(n+2) are all base-b Wieferich primes.

449, 226, 1207, 606, 3469, 653, 5649, 26645, 7805, 6154, 36088, 14368, 49662, 66565, 153463, 40667, 760637, 31871, 265418, 411467, 484205, 148989, 688285, 796095, 1920186, 747071, 3516680, 569812, 905979, 3193580, 3303343, 1967646, 1728157, 4436267, 912246

Offset: 1

Author

Felix Fröhlich, May 29 2021

Keywords

• nonn

Crossrefs

Cf. A039678, A259075. Column 3 of A286816.

Cf. smallest b > 1 such that prime(n+i) is a base-b Wieferich prime for each i = 0..k: A039678 (k=0), A259075 (k=1), A344828 (k=3), A344829 (k=4), A344830 (k=5), A344831 (k=6), A344832 (k=7).

Programs

PARI

a(n) = my(v=[prime(n)]); while(#v < 3, v=concat(v, nextprime(v[#v]+1))); for(b=2, oo, for(k=1, #v, if(Mod(b, v[k]^2)^(v[k]-1)!=1, break, if(k==#v, return(b)))))