A344832 a(n) is the smallest b > 1 such that prime(n), prime(n+1), prime(n+2), prime(n+3), prime(n+4), prime(n+5), prime(n+6) and prime(n+7) are all base-b Wieferich primes.

126664001, 230695118, 882345432, 12106746963, 93732236423, 66888229817, 84391291750, 3685694924698, 4506100208066, 1058174730735, 3827951700972, 58674393094169, 676579634125, 83450880181400, 100819901293157, 365919682326848, 695001153578920, 1046021079620904, 2989564836636529, 3724954519064878

Offset

1,1

Links

Max Alekseyev, Table of n, a(n) for n = 1..38

Prog

(PARI) a(n) = my(v=[prime(n)]); while(#v < 8, 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)))))

Crossrefs

Cf. A039678, A259075. Column 8 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), A344829 (k=4), A344830 (k=5), A344831 (k=6).

Sequence in context: A162450 A339537 A319065 * A334346 A115301 A256118

Adjacent sequences: A344829 A344830 A344831 * A344833 A344834 A344835

Keyword

nonn,hard

Author

Felix Fröhlich, May 29 2021

Extensions

Terms a(5) onward from Max Alekseyev, Oct 10 2023

Status

approved