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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. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 28 13:24 EDT 2020. Contains 337393 sequences. (Running on oeis4.)