A344829 a(n) is the smallest b > 1 such that prime(n), prime(n+1), prime(n+2), prime(n+3) and prime(n+4) are all base-b Wieferich primes.

19601, 54568, 13543, 296449, 3414284, 14380864, 3727271, 7916603, 65097619, 13793462, 152541840, 30495845, 91779237, 183068599, 558175167, 40698745, 825287029, 2151529020, 6271678163, 1266687934, 3149182509, 989067909, 10785363668, 18739432977, 4877709531, 24531035970, 11683733786, 52383593584

Offset: 1

Author

Felix Fröhlich, May 29 2021

Keywords

• nonn

Links

• Max Alekseyev, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A039678, A259075. Column 5 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), A344827 (k=2), A344828 (k=3), A344830 (k=5), A344831 (k=6), A344832 (k=7).

Programs

PARI

a(n) = my(v=[prime(n)]); while(#v < 5, 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)))))

Extensions

Terms a(22) onward from Max Alekseyev, Oct 10 2023