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A228828 Numbers n such that n^2 + pi(n) is prime. 1
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 (list; graph; refs; listen; history; text; internal format)
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 A006488 A121430

Adjacent sequences:  A228825 A228826 A228827 * A228829 A228830 A228831

KEYWORD

nonn

AUTHOR

K. D. Bajpai, Sep 04 2013

STATUS

approved

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Last modified September 16 12:28 EDT 2019. Contains 327098 sequences. (Running on oeis4.)