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A245061 Prime numbers p such that p - primepi(p) is a square, where primepi is the prime counting function. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 18 14:59 EST 2019. Contains 329262 sequences. (Running on oeis4.)