A245061 Prime numbers p such that p - primepi(p) is a square, where primepi is the prime counting function.

2, 3, 37, 541, 647, 881, 1151, 1301, 1627, 2377, 3271, 5179, 5641, 10501, 11597, 11821, 18503, 20543, 23339, 31259, 35461, 38669, 39499, 42901, 43331, 44201, 45523, 51973, 53407, 67213, 67757, 70489, 72169, 77291, 98893, 99551, 128291, 139721, 145207, 150011

Offset

1,1

Links

Chai Wah Wu, Table of n, a(n) for n = 1..500

Formula

a(n) = prime(A064370(n+1)). - Michel Marcus, Jul 11 2014

Example

37 is in the sequence because primepi(37) = 12, and 37 - 12 = 5^2.
541 is in the sequence because primepi(541) = 100, and 541 - 100 = 21^2.
547 is not in the sequence because primepi(547) = 101, and 547 - 101 = 446, which is not a perfect square.

Maple

with(numtheory): A245061:=n->`if`(type(sqrt(n-pi(n)), integer) and type(n, prime), n, NULL): seq(A245061(n), n=2..10^5); # Wesley Ivan Hurt, Jul 10 2014

Mathematica

Select[Prime[Range[200]], IntegerQ[Sqrt[# - PrimePi[#]]] &] (* Alonso del Arte, Jul 11 2014 *)

Prog

(PARI) select(p->issquare(p-primepi(p)), primes(15000)) \\ Michel Marcus, Jul 11 2014
(Python)
import sympy, gmpy2
[sympy.prime(n) for n in range(1, 10**6) if gmpy2.is_square(sympy.prime(n)-n)] # Chai Wah Wu, Jul 11 2014

Crossrefs

Cf. A104269, A113410, A064370.

Sequence in context: A061576 A221055 A144466 * A270587 A119448 A041329

Adjacent sequences: A245058 A245059 A245060 * A245062 A245063 A245064

Keyword

nonn

Author

Chai Wah Wu, Jul 10 2014

Extensions

More terms from Michel Marcus, Jul 11 2014

Status

approved