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 A109306 Numbers k such that k^2 + (k-1)^2 and k^2 + (k+1)^2 are both primes. 4
 2, 5, 25, 30, 35, 70, 85, 100, 110, 225, 230, 260, 285, 290, 320, 390, 410, 475, 490, 495, 515, 590, 680, 695, 710, 750, 760, 845, 950, 1080, 1100, 1135, 1175, 1190, 1195, 1270, 1295, 1305, 1330, 1365, 1410, 1475, 1715, 1750, 1785, 1845, 1855, 1925, 2015, 2060 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS All terms, except for the first one, are multiples of 5. All corresponding primes, except the first, end in 1. Cf. A027861, where in pairs of successive numbers the larger one is a multiple of 5 and is a term in this sequence. LINKS Daniel Starodubtsev, Table of n, a(n) for n = 1..10000 FORMULA a(n)^2 = A075577(n). - David A. Corneth, Apr 25 2021 EXAMPLE 25 is a term because 25^2 + 24^2 = 1201 and 25^2 + 26^2 = 1301 are both primes. MATHEMATICA Select[Range[2, 10000], PrimeQ[ #^2+(#+1)^2]&&PrimeQ[ #^2+(#-1)^2]&] PROG (PARI) for(k=1, 2060, my(j=2*k^2+1); if(isprime(j-2*k)&&isprime(j+2*k), print1(k, ", "))) \\ Hugo Pfoertner, Dec 07 2019 (Python) from sympy import isprime def aupto(limit): alst, is2 = [], False for k in range(1, limit+1): is1, is2 = is2, isprime(k**2 + (k+1)**2) if is1 and is2: alst.append(k) return alst print(aupto(2060)) # Michael S. Branicky, Apr 25 2021 CROSSREFS Cf. A027861, A075577. Sequence in context: A326971 A000895 A351895 * A009560 A333591 A079434 Adjacent sequences: A109303 A109304 A109305 * A109307 A109308 A109309 KEYWORD nonn AUTHOR Zak Seidov, Jun 25 2005 EXTENSIONS Definition corrected by Walter Kehowski, Jul 04 2005 STATUS approved

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Last modified March 24 09:15 EDT 2023. Contains 361470 sequences. (Running on oeis4.)