A247793 Least integer m > 0 such that pi(m*n) divides prime(m) + prime(n), where pi(x) denotes the number of primes not exceeding x.

2, 1, 75, 10, 18, 1, 75, 41, 58, 2, 94, 107, 14, 13, 2, 14, 14, 1, 84, 527, 124, 715, 13, 4, 1, 4, 276, 310, 2, 4, 11216, 3074, 3470, 14, 2, 15, 5, 947, 538839, 2, 8, 2, 1592, 4, 8, 16813, 2293, 1, 2755, 3007, 3272, 32203, 5357440, 6, 17, 17, 374252, 9, 17, 6905

Offset: 1

Author

Zhi-Wei Sun, Sep 23 2014

Keywords

• nonn

Comments

Conjecture: a(n) exists for any n > 0.

Examples

			a(4) = 10 since pi(4*10) = 12 divides prime(4) + prime(10) = 7 + 29 = 36.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..100
• Zhi-Wei Sun, A new theorem on the prime-counting function, arXiv:1409.5685, 2014.

Crossrefs

Cf. A000040, A000720, A247600, A247601, A247602, A247603, A247604, A247672, A247673.

Programs

Haskell

a247793_list = 2 : f (zip [2..] $ tail a000040_list) where
   f ((x, p) : xps) = m : f xps where
     m = head [y | y <- [1..], (p + a000040 y) `mod` a000720 (x * y) == 0]
-- Reinhard Zumkeller, Sep 24 2014

Mathematica

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