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A289829 Perfect squares of the form prime(k+1)^2 - prime(k)^2 + 1 where prime(k) is the k-th prime number. 1
25, 49, 121, 169, 289, 361, 841, 961, 1681, 1849, 2401, 2809, 3721, 5929, 6889, 7921, 8281, 10201, 11449, 11881, 14161, 14641, 17689, 24649, 26569, 32041, 38809, 41209, 43681, 44521, 61009, 63001, 69169, 76729, 80089, 85849, 89401, 94249, 96721, 97969, 108241 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..10000

EXAMPLE

7^2 - 5^2 + 1 = 5^2, 17^2 - 13^2 + 1 = 11^2, 47^2 - 43^2 + 1 = 19^2, etc.

MATHEMATICA

TakeWhile[#, # < 110000 &] &@ Union@ Select[Array[Prime[# + 1]^2 - Prime[#]^2 + 1 &, 10^4], IntegerQ@ Sqrt@ # &] (* Michael De Vlieger, Jul 13 2017 *)

PROG

(Python)

from __future__ import division

from sympy import divisors, isprime, prevprime, nextprime

A289829_list = []

for n in range(10**4):

    m = n**2-1

    for d in divisors(m):

        if d*d >= m:

            break

        r = m//d

        if not r % 2:

            r = r//2

            if not isprime(r):

                p, q = prevprime(r), nextprime(r)

                if m == (q-p)*(q+p):

                    A289829_list.append(n**2)

                    break # Chai Wah Wu, Jul 15 2017

(PARI) is(n) = if(!issquare(n), return(0), my(p=2); while(1, if(n==nextprime(p+1)^2-p^2+1, return(1)); p=nextprime(p+1); if(p > n, return(0)))) \\ Felix Fröhlich, Jul 15 2017

CROSSREFS

Sequence in context: A106564 A308177 A104777 * A131706 A110015 A110586

Adjacent sequences:  A289826 A289827 A289828 * A289830 A289831 A289832

KEYWORD

nonn

AUTHOR

Joseph Wheat, Jul 12 2017

EXTENSIONS

More terms from Alois P. Heinz, Jul 13 2017

STATUS

approved

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Last modified August 10 06:08 EDT 2022. Contains 356029 sequences. (Running on oeis4.)