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 A075577 k^2 is a term if k^2 + (k-1)^2 and k^2 + (k+1)^2 are primes. 3
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified February 28 07:05 EST 2024. Contains 370387 sequences. (Running on oeis4.)