A247793 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.

2, 1, 75, 10, 18, 1, 75, 41, 58, 2, 94, 107, 14, 13, 2, 14, 14, 1, 84, 527, 124, 715, 13, 4, 1, 4, 276, 310, 2, 4, 11216, 3074, 3470, 14, 2, 15, 5, 947, 538839, 2, 8, 2, 1592, 4, 8, 16813, 2293, 1, 2755, 3007, 3272, 32203, 5357440, 6, 17, 17, 374252, 9, 17, 6905

Offset

1,1

Comments

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

Links

Zhi-Wei Sun, Table of n, a(n) for n = 1..100

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

Example

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

Mathematica

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}]

Prog

(Haskell)
a247793_list = 2 : f (zip [2..] $ tail a000040_list) where
   f ((x, p) : xps) = m : f xps where
     m = head [y | y <- [1..], (p + a000040 y) `mod` a000720 (x * y) == 0]
-- Reinhard Zumkeller, Sep 24 2014

Crossrefs

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

Sequence in context: A284596 A216485 A096681 * A067276 A118580 A118558

Adjacent sequences: A247790 A247791 A247792 * A247794 A247795 A247796

Keyword

nonn

Author

Zhi-Wei Sun, Sep 23 2014

Status

approved