Search: id:A143851
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%I A143851
%S A143851 2,13,167,2239,439867
%N A143851 Primes that divide the sum of their residues modulo all smaller primes
%C A143851 No other terms below 10^7. [From Max Alekseyev (maxale(AT)gmail.com), 
               Sep 13 2009]
%C A143851 10^8 < a(6) <= 724031017. a(7) <= 1990127567. [From Donovan Johnson (donovan.johnson(AT)yahoo.com), 
               Nov 25 2009]
%F A143851 Primes p such that p divides A034387([p/1]) + A034387([p/2]) + ... + 
               A034387([p/p]) = A034387([p/1]) + ... + A034387([p/m]) - m*A034387(m) 
               + \sum_{prime q<=m} q*[p/q], where m = [sqrt(p)]. [From Max Alekseyev 
               (maxale(AT)gmail.com), Sep 13 2009]
%e A143851 13 is congruent to 1,1,3,6 and 2, mod 2,3,5,7 and 11 respectively. 1+1+3+6+2=13, 
               which is a multiple of the original number, 13. So the original number, 
               is in the sequence.
%t A143851 For[n = 1, n < 1000001, n++, p = Prime[n]; m = Mod[Sum[Mod[p, Prime[i]], 
               {i, 1, n - 1}], p]; If[m == 0, Print[p]]]
%Y A143851 Cf. A065132
%Y A143851 Sequence in context: A090643 A132521 A078363 this_sequence A088316 A006905 
               A119400
%Y A143851 Adjacent sequences: A143848 A143849 A143850 this_sequence A143852 A143853 
               A143854
%K A143851 more,nonn,new
%O A143851 1,1
%A A143851 N. Fernandez (ncf(AT)borve.org), Sep 03 2008

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