A247600 Least positive integer m with pi(m*n) = m + n, where pi(x) denotes the number of primes not exceeding x.

9, 7, 6, 998, 5, 5, 5, 5, 5, 5, 636787, 1617099, 4124188, 10553076, 5, 5, 179992154, 465769460, 1208198239, 3140421185, 5, 5, 5, 145935688930, 5, 5, 5, 5, 5, 5, 5, 5, 5

Offset

5,1

Comments

The author proved that a(n) exists for every n >= 5.

a(39) = a(41) = 5. - Chai Wah Wu, Jun 06 2024

Links

Table of n, a(n) for n=5..37.

Zhi-Wei Sun, A new theorem on the prime-counting function, arXiv:1409.5685 [math.NT], 2014-2017.

Example

a(5) = 9 since pi(5*9) = 14 = 5 + 9, and pi(5*m) = 5 + m for no m < 9.

Mathematica

Do[m=1; Label[aa]; If[PrimePi[n*m]==m+n, Print[n, " ", m]; Goto[bb]]; m=m+1; Goto[aa]; Label[bb]; Continue, {n, 5, 21}]
Table[m = 1; While[PrimePi[m*n] != m + n, m++]; m, {n, 5, 14}] (* Robert Price, Mar 20 2019 *)

Crossrefs

Cf. A247601, A247602, A247603, A247604, A000720, A281197.

Sequence in context: A154678 A021915 A163828 * A281197 A373507 A199503

Adjacent sequences: A247597 A247598 A247599 * A247601 A247602 A247603

Keyword

nonn,more

Author

Zhi-Wei Sun, Sep 21 2014

Extensions

a(22)-a(37) from Chai Wah Wu, May 03 2018

Status

approved