A247975 - OEIS

%I #21 Jan 04 2018 17:28:36

%S 1,8,15479,30,29,68,51,2,73,15,39,13,12,36,10,25,33,8,15,38,40,108,42,

%T 1,16,39,31,57,5,4,27,2,17,51,30,14,36,20,11,21,32,23,39,689,29,4,27,

%U 1873,184,7248,7,153,132,76,75,18,28,99,2,86

%N Least positive integer m such that m + n divides prime(m)^2 + prime(n)^2.

%C Conjecture: a(n) exists for any n > 0. - _Zhi-Wei Sun_, Sep 28 2014

%C If a(i) = j, then a(j) <= i. - _Derek Orr_, Sep 28 2014

%H Chai Wah Wu, <a href="/A247975/b247975.txt">Table of n, a(n) for n = 1..10000</a> (n = 1..5000 from Zhi-Wei Sun)

%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(2) = 8 since 8 + 2 = 10 divides prime(8)^2 + prime(2)^2 = 19^2 + 3^2 = 370.

%e a(3) = 15479 since 15479 + 3 = 15482 divides prime(15479)^2 + prime(3)^2 = 169789^2 + 5^2 = 28828304546 = 15482*1862053.

%e a(4703) = 760027770 since 760027770 + 4703 = 760032473 divides prime(760027770)^2 + prime(4703)^2 = 17111249191^2 + 45329^2 = 292794848878552872722 = 760032473*385239919714.

%t Do[m = 1; Label[aa]; If[Mod[Prime[m]^2 + Prime[n]^2, m + n] == 0, Print[n, " ", m]; Goto[bb]]; m = m + 1; Goto[aa]; Label[bb]; Continue, {n, 1, 60}]

%o (PARI)

%o a(n)=m=1;while((prime(m)^2+prime(n)^2)%(m+n),m++);m

%o vector(75,n,a(n)) \\ _Derek Orr_, Sep 28 2014

%Y Cf. A000040, A247824.

%K nonn

%O 1,2

%A _Zhi-Wei Sun_, Sep 28 2014