A247793 - OEIS

%I #12 Sep 24 2014 09:36:01

%S 2,1,75,10,18,1,75,41,58,2,94,107,14,13,2,14,14,1,84,527,124,715,13,4,

%T 1,4,276,310,2,4,11216,3074,3470,14,2,15,5,947,538839,2,8,2,1592,4,8,

%U 16813,2293,1,2755,3007,3272,32203,5357440,6,17,17,374252,9,17,6905

%N 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.

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

%H Zhi-Wei Sun, <a href="/A247793/b247793.txt">Table of n, a(n) for n = 1..100</a>

%H Zhi-Wei Sun, <a href="http://arxiv.org/abs/1409.5685">A new theorem on the prime-counting function</a>, arXiv:1409.5685, 2014.

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

%t 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}]

%o (Haskell)

%o a247793_list = 2 : f (zip [2..] $ tail a000040_list) where

%o    f ((x, p) : xps) = m : f xps where

%o      m = head [y | y <- [1..], (p + a000040 y) `mod` a000720 (x * y) == 0]

%o -- _Reinhard Zumkeller_, Sep 24 2014

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

%K nonn

%O 1,1

%A _Zhi-Wei Sun_, Sep 23 2014