A228828 Numbers n such that n^2 + pi(n) is prime.

2, 3, 7, 12, 18, 21, 36, 37, 42, 45, 52, 55, 60, 61, 65, 68, 70, 79, 84, 95, 98, 113, 130, 135, 143, 145, 155, 180, 181, 185, 195, 205, 216, 222, 231, 239, 253, 262, 273, 275, 325, 332, 334, 354, 368, 370, 385, 402, 417, 421, 432, 433, 454, 462, 488, 505, 516

Offset

1,1

Comments

Conjecture: the sequence is infinite.

Links

K. D. Bajpai and  Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 3000 terms from Bajpai)

Example

a(6) = 21 :  n^2+pi(n ) = 21^2 + pi(21) = 441+8 = 449 which is a prime.

Maple

with(numtheory): KD:= proc() local a;  a:= n^2+pi(n); if isprime(a) then RETURN(n): fi; end: seq(KD(), n=1..2000);

Mathematica

Select[Range[600], PrimeQ[#^2+PrimePi[#]]&] (* Harvey P. Dale, Jul 04 2018 *)

Prog

(PARI) v=List(); p=0; for(n=2, 1e4, p+=isprime(n); if(isprime(n^2+p), listput(v, n))); Vec(v) \\ Charles R Greathouse IV, Sep 04 2013

Crossrefs

Cf. A064711, A064712.

Cf. A077510 (numbers n such that n + pi(n) is a prime).

Sequence in context: A066733 A049623 A302506 * A061577 A350437 A006488

Adjacent sequences: A228825 A228826 A228827 * A228829 A228830 A228831

Keyword

nonn

Author

K. D. Bajpai, Sep 04 2013

Status

approved