Search: id:A125854
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%I A125854
%S A125854 3,29,37,3373,2001907169
%N A125854 Primes p with the property that p divides the Wolstenholme number A001008((p+1)/
               2).
%C A125854 Note that if prime p>3 divides A001008((p+1)/2) then it also divides 
               A001008((p-3)/2).
%C A125854 Note that for a prime p, H([p/2]) == 2*(2^(-p(p-1))-1)/p^2 (mod p). Therefore 
               a prime p divides the Wolstenholme number A001008((p+1)/2) if and 
               only if 2^(-p(p-1)) == 1-p^2 (mod p^3) or, equivalently, 2^(p-1) 
               == 1+p (mod p^2).
%C A125854 Disjunctive union of the sequences A154998 and A121999 that contain primes 
               congruent respectively to 1,3 and 5,7 modulo 8. (Alekseyev)
%C A125854 No other terms below 10^11. (Alekseyev)
%e A125854 a(1) = 3 because prime 3 divides A001008(2) = 3 and there is no p<3 that 
               divides A001008((p+1)/2).
%e A125854 a(2) = 29 because 29 divides A001008(15) = 1195757; but there is no prime 
               p (3<p<29) that divides A001008((p+1)/2).
%Y A125854 Cf. A001008, A121999, A014566, A154998
%Y A125854 Sequence in context: A030274 A055062 A086174 this_sequence A167278 A106979 
               A087209
%Y A125854 Adjacent sequences: A125851 A125852 A125853 this_sequence A125855 A125856 
               A125857
%K A125854 hard,more,nonn
%O A125854 1,1
%A A125854 Alexander Adamchuk (alex(AT)kolmogorov.com), Dec 11 2006
%E A125854 Entry revised and a(5)=2001907169 provided by Max Alekseyev (maxale(AT)gmail.com), 
               Jan 18 2009
%E A125854 Edited by Max Alekseyev (maxale(AT)gmail.com), Oct 13 2009

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