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
Keywords
Examples
37 is a term because 37 is 12th prime and 37 + 12 = 49 = 7^2.
Programs
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Maple
q:= n-> isprime(n) and issqr(n+numtheory[pi](n)): select(q, [$0..150000])[]; # Alois P. Heinz, Oct 27 2021
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Mathematica
Select[Prime@Range[10^4],IntegerQ@Sqrt[PrimePi@#+#]&] (* Giorgos Kalogeropoulos, Oct 26 2021 *)
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PARI
isok(n) = isprime(n) && issquare(n + primepi(n)); \\ Michel Marcus, Oct 05 2013
Formula
a(n) = A086968(n)^2 - pi(a(n)).
Extensions
Definition corrected by Michel Marcus, Oct 05 2013
Comments