A248197 Least positive integer m such that m + n divides prime(prime(m)) + prime(prime(n)).

1, 9, 4, 1, 17, 12, 3, 4, 2, 4, 15, 6, 1, 20, 4, 74, 4, 3, 2, 8, 9, 5, 3, 17, 5, 9, 8, 26, 8, 1, 14, 4, 17, 35, 33, 52, 29, 46, 35, 95, 4, 4, 23, 24, 23, 38, 135, 64, 11, 62, 222, 36, 92, 41, 1, 39, 6, 37, 3, 18

Offset: 1

Author

Zhi-Wei Sun, Oct 03 2014

Keywords

• nonn

Comments

Conjecture: a(n) exists for any n > 0. Moreover, a(n) < n*(n-1) if n > 2.

Examples

			a(3) = 4 since 3 + 4 = 7 divides prime(prime(3)) + prime(prime(4)) = prime(5) + prime(7) = 11 + 17 = 28.
a(2479) = 3386154 since 2479 + 3386154 = 3388633 divides prime(prime(2479)) + prime(prime(3386154)) = prime(22111) + prime(56851657) = 250963 + 1124775193 = 1125026156 = 332*3388633.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..10000
• Zhi-Wei Sun, A new theorem on the prime-counting function, arXiv:1409.5685, 2014.

Crossrefs

Cf. A000040, A247824, A247975.

Programs

Mathematica

Do[m=1;Label[aa];If[Mod[Prime[Prime[m]]+Prime[Prime[n]],m+n]==0,Print[n," ",m];Goto[bb]];m=m+1;Goto[aa];Label[bb];Continue,{n,1,60}]