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%I #15 Mar 25 2016 07:49:51
%S 2,2,2,3,2,2,2,3,2,2,2,3,2,2,2,5,2,2,2,3,2,2,2,3,2,2,2,3,2,2,2,3,2,2,
%T 2,5,2,2,2,3,2,2,2,3,2,2,2,3,2,2,2,5,2,2,2,3,2,2,2,3,2,2,2,3,2,2,2,3,
%U 2,2,2,5,2,2,2,3,2,2,2,3,2,2,2,3,2,2,2
%N Smallest non-Wieferich prime to base n, i.e., smallest prime p such that n^(p-1) =/= 1 (mod p^2).
%C A256236 gives the smallest i such that a(i) = A000040(n).
%C a(n) > 2 iff A039951(n) = 2.
%C a(n) > 3 iff A268352(n) = 3.
%C Does every prime appear in the sequence?
%C It is easy to see that the answer to the previous question is "yes" if and only if A256236 is infinite.
%C The ABC-(k, Epsilon) conjecture with k >= 2 and Epsilon > 0 such that 1/(1/Epsilon + 1) + 1/k <= log(2)/(24*log(a)) implies that a(n) exists for all n (cf. Broughan, 2006; theorem 5.6).
%H Felix Fröhlich, <a href="/A270776/b270776.txt">Table of n, a(n) for n = 2..10000</a>
%H K. A. Broughan, <a href="http://nzjm.math.auckland.ac.nz/images/d/d6/Relaxations_of_the_ABC_Conjecture_using_integer_k%27th_roots.pdf">Relaxations of the abc conjecture using integer k'th roots</a>, New Zealand Journal of Mathematics, 35 (2006), 121-136.
%e The sequence of base-17 Wieferich primes (A128668) starts 2, 3, 46021. Thus the smallest non-Wieferich prime to base 17 is 5 and hence a(17) = 5.
%o (PARI) a(n) = forprime(p=1, , if(Mod(n, p^2)^(p-1)!=1, return(p)))
%Y Cf. A039951, A256236, A268352.
%K nonn
%O 2,1
%A _Felix Fröhlich_, Mar 22 2016
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