A109307 Numbers m such that m^2 + (m+/-1)^2 are both semiprimes.

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

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: A371187 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