A247975 Least positive integer m such that m + n divides prime(m)^2 + prime(n)^2.

1, 8, 15479, 30, 29, 68, 51, 2, 73, 15, 39, 13, 12, 36, 10, 25, 33, 8, 15, 38, 40, 108, 42, 1, 16, 39, 31, 57, 5, 4, 27, 2, 17, 51, 30, 14, 36, 20, 11, 21, 32, 23, 39, 689, 29, 4, 27, 1873, 184, 7248, 7, 153, 132, 76, 75, 18, 28, 99, 2, 86

Offset: 1

Author

Zhi-Wei Sun, Sep 28 2014

Keywords

• nonn

Comments

Conjecture: a(n) exists for any n > 0. - Zhi-Wei Sun, Sep 28 2014

If a(i) = j, then a(j) <= i. - Derek Orr, Sep 28 2014

Examples

			a(2) = 8 since 8 + 2 = 10 divides prime(8)^2 + prime(2)^2 = 19^2 + 3^2 = 370.
a(3) = 15479 since 15479 + 3 = 15482 divides prime(15479)^2 + prime(3)^2 = 169789^2 + 5^2 = 28828304546 = 15482*1862053.
a(4703) = 760027770 since 760027770 + 4703 = 760032473 divides prime(760027770)^2 + prime(4703)^2 = 17111249191^2 + 45329^2 = 292794848878552872722 = 760032473*385239919714.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000 (n = 1..5000 from Zhi-Wei Sun)
• Zhi-Wei Sun, A new theorem on the prime-counting function, arXiv:1409.5685, 2014.

Crossrefs

Cf. A000040, A247824.

Programs

Mathematica

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}]

PARI

a(n)=m=1;while((prime(m)^2+prime(n)^2)%(m+n),m++);m
vector(75,n,a(n)) \\ Derek Orr, Sep 28 2014