A099481 Numbers k such that 2^k - k^2 is a semiprime.

11, 13, 15, 21, 23, 37, 39, 41, 43, 47, 49, 55, 67, 75, 103, 105, 133, 147, 153, 161, 163, 177, 201, 209, 221, 239, 249, 263, 311, 335, 355, 397, 413, 421, 437, 447, 583, 617, 775, 807

Offset: 1

Author

Hugo Pfoertner, Oct 18 2004

Keywords

• nonn
• more
• hard

Comments

The smaller prime factor of the 125-digit semiprime 2^413 - 413^2 has 40 digits; for the 127-digit semiprime 2^421 - 421^2 the smaller prime factor has 45 digits. The next term is >= 583. - Hugo Pfoertner, Oct 14 2007

The factorization of the 176-decimal-digit composite 2^583 - 583^2 using SNFS in YAFU took 55000 seconds on 4 cores of an i5-2400 CPU @ 3.10GHz. a(38) >= 617. - Hugo Pfoertner, Jul 23 2019

a(41) >= 827. - Hugo Pfoertner, Jul 26 2019

Examples

			a(1) = 11 because 2^11 - 11^2 = 1927 = 41*47.
		

Links

• Dario Alpern, Factorization using the Elliptic Curve Method.
• factordb, Status of 2^583-583^2 in factordb.com.
• factordb, Status of 2^617-617^2 in factordb.com.
• factordb, Status of 2^827-827^2 in factordb.com.
• YAFU, Automated integer factorization.

Crossrefs

Cf. A024012 (2^n-n^2), A099482 (semiprimes of the form 2^n-n^2), A072180 (2^n-n^2 is prime), A075896 (primes of the form 2^n-n^2).

Extensions

More terms from Hugo Pfoertner, Oct 14 2007

a(37)-a(40) from Hugo Pfoertner, Jul 26 2019