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A248052 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. 3
1, 2, 1, 8, 7, 7, 5, 1, 25, 35, 15, 14, 13, 12, 1, 4, 23, 532, 22, 385, 113, 1, 17, 138, 8, 92, 80, 44, 116, 128, 586, 165, 5, 464, 10, 39, 80, 38, 1, 52, 33, 118, 6, 28, 11, 1239, 47, 92, 517, 3, 145, 40, 8, 184, 104, 104, 16, 73, 53, 52, 5, 145, 172, 68, 11 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

(ii) For each integer m > 0, there is a positive integer n such that m + n divides prime(m^2) + prime(n^2).

LINKS

Zhi-Wei Sun, Table of n, a(n) for n = 1..1000

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

EXAMPLE

a(4) = 8 since 8 + 4 = 12 divides pi(8^2) + pi(4^2) = 18 + 6 = 24.

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, 70}]

a[ n_] := If[ n<1, 0, Module[ {m=1}, While[ Not @ Divisible[ PrimePi[m^2] + PrimePi[n^2], m + n], m++]; m]]; (* Michael Somos, Sep 30 2014 *)

CROSSREFS

Cf. A000040, A000720, A247824, A247975, A248044, A248054.

Sequence in context: A168142 A081800 A254180 * A105672 A214271 A262007

Adjacent sequences:  A248049 A248050 A248051 * A248053 A248054 A248055

KEYWORD

nonn

AUTHOR

Zhi-Wei Sun, Sep 30 2014

STATUS

approved

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Last modified January 27 14:39 EST 2020. Contains 331295 sequences. (Running on oeis4.)