cp's OEIS Frontend

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.

%I A344831 #13 Oct 11 2023 09:43:38
%S A344831 4486949,20950343,23250274,741652533,710808570,2380570527,4967352848,
%T A344831 39489360341,6143373023,64470545267,627069771908,407165268367,
%U A344831 676579634125,676579634125,2923957743077,369072416795,5110842013966,19645397150616,16037329738682,5867065121893,31015370285102
%N 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.
%C A344831 Surprisingly, we have a(13) = a(14) = A344832(13). - _Max Alekseyev_, Oct 10 2023
%H A344831 Max Alekseyev, <a href="/A344831/b344831.txt">Table of n, a(n) for n = 1..50</a>
%o A344831 (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)))))
%Y A344831 Cf. A039678, A259075. Column 7 of A286816.
%Y A344831 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).
%K A344831 nonn
%O A344831 1,1
%A A344831 _Felix Fröhlich_, May 29 2021
%E A344831 Terms a(8) onward from _Max Alekseyev_, Oct 10 2023