A344831 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) and prime(n+6) are all base-b Wieferich primes.

4486949, 20950343, 23250274, 741652533, 710808570, 2380570527, 4967352848, 39489360341, 6143373023, 64470545267, 627069771908, 407165268367, 676579634125, 676579634125, 2923957743077, 369072416795, 5110842013966, 19645397150616, 16037329738682, 5867065121893, 31015370285102

Offset: 1

Author

Felix Fröhlich, May 29 2021

Keywords

• nonn

Comments

Surprisingly, we have a(13) = a(14) = A344832(13). - Max Alekseyev, Oct 10 2023

Links

• Max Alekseyev, Table of n, a(n) for n = 1..50

Crossrefs

Cf. A039678, A259075. Column 7 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), A344832 (k=7).

Programs

PARI

a(n) = my(v=[prime(n)]); while(#v < 7, 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(8) onward from Max Alekseyev, Oct 10 2023