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 A109307 Numbers m such that m^2 + (m+/-1)^2 are both semiprimes. 0
 11, 16, 27, 38, 44, 45, 52, 55, 56, 57, 63, 64, 68, 74, 75, 76, 77, 81, 112, 113, 114, 124, 134, 141, 142, 143, 148, 151, 152, 170, 180, 181, 182, 183, 184, 191, 192, 209, 214, 215, 216, 227, 240, 251, 252, 255, 256, 263, 266, 269, 270, 274, 275, 293, 294, 295 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS EXAMPLE 38 is a term because 38^2 + 37^2 = 2813 = 29*97 (semiprime) and 38^2 + 39^2 = 2965 = 5*593 (semiprime). MATHEMATICA Select[Range[2, 400], Plus@@Last/@FactorInteger[ #^2+(#+1)^2]==Plus@@Last/@FactorInteger[ #^2+(#-1)^2]==2&] PROG (Python) from sympy import factorint def issemiprime(n): return sum(factorint(n).values()) == 2 def ok(n): return all(issemiprime(n**2 + (n+k)**2) for k in [1, -1]) print([k for k in range(296) if ok(k)]) # Michael S. Branicky, Nov 16 2021 CROSSREFS Sequence in context: A258588 A110031 A166451 * A327752 A128835 A316171 Adjacent sequences: A109304 A109305 A109306 * A109308 A109309 A109310 KEYWORD nonn AUTHOR Zak Seidov, Jun 25 2005 EXTENSIONS Title corrected by Michael S. Branicky, Nov 16 2021 STATUS approved

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Last modified March 22 07:34 EDT 2023. Contains 361413 sequences. (Running on oeis4.)