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%I #10 Nov 16 2021 07:34:57
%S 11,16,27,38,44,45,52,55,56,57,63,64,68,74,75,76,77,81,112,113,114,
%T 124,134,141,142,143,148,151,152,170,180,181,182,183,184,191,192,209,
%U 214,215,216,227,240,251,252,255,256,263,266,269,270,274,275,293,294,295
%N Numbers m such that m^2 + (m+/-1)^2 are both semiprimes.
%e 38 is a term because 38^2 + 37^2 = 2813 = 29*97 (semiprime) and 38^2 + 39^2 = 2965 = 5*593 (semiprime).
%t Select[Range[2, 400], Plus@@Last/@FactorInteger[ #^2+(#+1)^2]==Plus@@Last/@FactorInteger[ #^2+(#-1)^2]==2&]
%o (Python)
%o from sympy import factorint
%o def issemiprime(n): return sum(factorint(n).values()) == 2
%o def ok(n): return all(issemiprime(n**2 + (n+k)**2) for k in [1, -1])
%o print([k for k in range(296) if ok(k)]) # _Michael S. Branicky_, Nov 16 2021
%K nonn
%O 1,1
%A _Zak Seidov_, Jun 25 2005
%E Title corrected by _Michael S. Branicky_, Nov 16 2021
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