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A274423 Let s(n,j) be Sum_{i=1..j} (prime(primepi(n) + i) mod n). Numbers n such that there exists j with s(n,j) = n.

%I A274423 #18 Jun 22 2016 23:48:43
%S A274423 2,3,4,6,8,44,48,66,90,108,156,206,284,854,1002,1188,1194,1212,1320,
%T A274423 2234,2460,2792,3336,3478,7096,7164,7218,7236,7752,8304,9164,10272,
%U A274423 12090,12594,13322,15530,17038,17162,18026,18212,20412,20494,21966,23374,23518,24664
%N A274423 Let s(n,j) be Sum_{i=1..j} (prime(primepi(n) + i) mod n). Numbers n such that there exists j with s(n,j) = n.
%H A274423 Paolo P. Lava, <a href="/A274423/b274423.txt">Table of n, a(n) for n = 1..200</a>
%H A274423 Paolo P. Lava, <a href="/A274423/a274423.txt">First 200 terms with the number of primes j</a>
%e A274423 47 mod 44 + 53 mod 44 + 59 mod 44 + 61 mod 44 = 3 + 9 + 15 + 17 = 44.
%p A274423 P:=proc(q) local a,b,k,n; for n from 2 to q do a:=0;
%p A274423 b:=nextprime(n); while n>a do a:=a+(b mod n); b:=nextprime(b); od;
%p A274423 if n=a then print(n); fi; od; end: P(10^9);
%Y A274423 Cf. A000040, A024934, A274422, A274424.
%K A274423 nonn,easy
%O A274423 1,1
%A A274423 _Paolo P. Lava_, Jun 21 2016
%E A274423 Name corrected by _David A. Corneth_, Jun 22 2016