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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.

%I A344832 #14 Oct 13 2023 07:52:04
%S A344832 126664001,230695118,882345432,12106746963,93732236423,66888229817,
%T A344832 84391291750,3685694924698,4506100208066,1058174730735,3827951700972,
%U A344832 58674393094169,676579634125,83450880181400,100819901293157,365919682326848,695001153578920,1046021079620904,2989564836636529,3724954519064878
%N 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.
%H A344832 Max Alekseyev, <a href="/A344832/b344832.txt">Table of n, a(n) for n = 1..38</a>
%o A344832 (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)))))
%Y A344832 Cf. A039678, A259075. Column 8 of A286816.
%Y A344832 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).
%K A344832 nonn,hard
%O A344832 1,1
%A A344832 _Felix Fröhlich_, May 29 2021
%E A344832 Terms a(5) onward from _Max Alekseyev_, Oct 10 2023