A075577 k^2 is a term if k^2 + (k-1)^2 and k^2 + (k+1)^2 are primes.

4, 25, 625, 900, 1225, 4900, 7225, 10000, 12100, 50625, 52900, 67600, 81225, 84100, 102400, 152100, 168100, 225625, 240100, 245025, 265225, 348100, 462400, 483025, 504100, 562500, 577600, 714025, 902500, 1166400, 1210000, 1288225, 1380625, 1416100, 1428025

Offset: 1

Author

Amarnath Murthy, Sep 25 2002

Keywords

• nonn

Comments

For a(2) onwards, a(n) == 0 (mod 25).

Examples

			900 = 30^2 is a term because 30^2 + 29^2 = 1741 is prime and 30^2 + 31^2 = 1861 is prime.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A109306.

Programs

Mathematica

Do[s=n^2+(n-1)^2; s1=n^2+(n+1)^2; If[PrimeQ[s]&&PrimeQ[s1], Print[n^2]], {n, 1, 5000}]

Python

from sympy import isprime
def aupto(limit):
  alst, is2 = [], False
  for k in range(1, int(limit**.5) + 2):
    is1, is2 = is2, isprime(k**2 + (k+1)**2)
    if is1 and is2: alst.append(k**2)
  return alst
print(aupto(1500000)) # Michael S. Branicky, Apr 25 2021

Formula

a(n) = A109306(n)^2. - David A. Corneth, Apr 25 2021

Extensions

More terms from Labos Elemer, Sep 27 2002

a(34) and beyond from Michael S. Branicky, Apr 25 2021