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.

2, 3, 4, 6, 8, 44, 48, 66, 90, 108, 156, 206, 284, 854, 1002, 1188, 1194, 1212, 1320, 2234, 2460, 2792, 3336, 3478, 7096, 7164, 7218, 7236, 7752, 8304, 9164, 10272, 12090, 12594, 13322, 15530, 17038, 17162, 18026, 18212, 20412, 20494, 21966, 23374, 23518, 24664

Offset: 1

Author

Paolo P. Lava, Jun 21 2016

Keywords

• nonn
• easy

Examples

			47 mod 44 + 53 mod 44 + 59 mod 44 + 61 mod 44 = 3 + 9 + 15 + 17 = 44.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..200
• Paolo P. Lava, First 200 terms with the number of primes j

Crossrefs

Cf. A000040, A024934, A274422, A274424.

Programs

Maple

P:=proc(q) local a,b,k,n; for n from 2 to q do a:=0;
b:=nextprime(n); while n>a do a:=a+(b mod n); b:=nextprime(b); od;
if n=a then print(n); fi; od; end: P(10^9);

Extensions

Name corrected by David A. Corneth, Jun 22 2016