A248044 Least positive integer m such that m + n divides pi(m)^2 + pi(n)^2, where pi(x) denotes the number of primes not exceeding x.

1, 3, 1, 4, 12, 11, 1, 8, 7, 16, 2, 5, 26, 25, 24, 4, 228, 227, 46, 45, 44, 43, 16, 6, 5, 1, 27, 26, 45, 44, 12526, 12525, 12524, 12523, 2970, 502, 351, 350, 46, 45, 236, 235, 10, 9, 8, 4, 1078, 1077, 576, 575, 574, 198, 63, 62, 61, 176, 16, 10, 362, 70

Offset

1,2

Comments

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

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000 (n = 1..1387 from Zhi-Wei Sun)

Zhi-Wei Sun, A new theorem on the prime-counting function, arXiv:1409.5685, 2014.

Example

a(5) = 12 since 12 + 5 = 17 divides pi(12)^2 + pi(5)^2 = 5^2 + 3^2 = 34.

Mathematica

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

Crossrefs

Cf. A000720, A247824, A247975, A248035, A248036.

Sequence in context: A065253 A010756 A191857 * A153278 A010284 A095328

Adjacent sequences: A248041 A248042 A248043 * A248045 A248046 A248047

Keyword

nonn,look

Author

Zhi-Wei Sun, Sep 30 2014

Status

approved