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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

Table of n, a(n) for n=1..56.

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.)