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

1,1

Comments

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

Links

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

Formula

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

Example

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

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}]

Prog

(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

Crossrefs

Cf. A109306.

Sequence in context: A086216 A167041 A123129 * A004019 A302092 A277110

Adjacent sequences: A075574 A075575 A075576 * A075578 A075579 A075580

Keyword

nonn

Author

Amarnath Murthy, Sep 25 2002

Extensions

More terms from Labos Elemer, Sep 27 2002

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

Status

approved