A104269 Prime numbers p such that primepi(p) + p is a square.

11, 37, 443, 571, 1049, 1307, 1451, 1523, 2837, 3593, 5233, 8539, 9257, 9439, 10391, 10987, 17579, 21881, 23321, 23909, 25117, 30557, 30893, 31231, 42239, 47123, 64811, 65789, 83089, 91631, 92219, 95747, 97549, 99971, 101197, 101807, 110603, 114487, 120431

Offset

1,1

Comments

A064371(p) + A000040(A064371(p)) = A086968(p)^2.

p^2 is prime + its index A086968; p + p-th prime is a square A064371.

Equals the prime terms of A073945. - Bill McEachen, Oct 26 2021

Links

Table of n, a(n) for n=1..39.

Formula

a(n) = A086968(n)^2 - pi(a(n)).

Example

37 is a term because 37 is 12th prime and 37 + 12 = 49 = 7^2.

Maple

q:= n-> isprime(n) and issqr(n+numtheory[pi](n)):
select(q, [$0..150000])[];  # Alois P. Heinz, Oct 27 2021

Mathematica

Select[Prime@Range[10^4], IntegerQ@Sqrt[PrimePi@#+#]&] (* Giorgos Kalogeropoulos, Oct 26 2021 *)

Prog

(PARI) isok(n) = isprime(n) && issquare(n + primepi(n)); \\ Michel Marcus, Oct 05 2013

Crossrefs

Cf. A000040, A000720, A064371, A086968, A064370, A073945.

Sequence in context: A261420 A034969 A052432 * A084014 A232976 A084018

Adjacent sequences: A104266 A104267 A104268 * A104270 A104271 A104272

Keyword

nonn

Author

Zak Seidov, Feb 26 2005

Extensions

Definition corrected by Michel Marcus, Oct 05 2013

Status

approved