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A109307
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Numbers m such that m^2 + (m+/-1)^2 are both semiprimes.
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0
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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
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OFFSET
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1,1
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LINKS
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EXAMPLE
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38 is a term because 38^2 + 37^2 = 2813 = 29*97 (semiprime) and 38^2 + 39^2 = 2965 = 5*593 (semiprime).
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MATHEMATICA
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Select[Range[2, 400], Plus@@Last/@FactorInteger[ #^2+(#+1)^2]==Plus@@Last/@FactorInteger[ #^2+(#-1)^2]==2&]
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PROG
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(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])
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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