A099481 - OEIS

%I #29 Jul 08 2023 18:09:33

%S 11,13,15,21,23,37,39,41,43,47,49,55,67,75,103,105,133,147,153,161,

%T 163,177,201,209,221,239,249,263,311,335,355,397,413,421,437,447,583,

%U 617,775,807

%N Numbers k such that 2^k - k^2 is a semiprime.

%C 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

%C 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

%C a(41) >= 827. - _Hugo Pfoertner_, Jul 26 2019

%H Dario Alpern, <a href="https://www.alpertron.com.ar/ECM.HTM">Factorization using the Elliptic Curve Method</a>.

%H factordb, <a href="http://factordb.com/index.php?query=2%5E583-583%5E2">Status of 2^583-583^2 in factordb.com</a>.

%H factordb, <a href="http://factordb.com/index.php?query=2%5E617-617%5E2">Status of 2^617-617^2 in factordb.com</a>.

%H factordb, <a href="http://factordb.com/index.php?query=2%5E827-827%5E2">Status of 2^827-827^2 in factordb.com</a>.

%H YAFU, <a href="https://sourceforge.net/projects/yafu/">Automated integer factorization</a>.

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

%Y 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).

%K nonn,more,hard

%O 1,1

%A _Hugo Pfoertner_, Oct 18 2004

%E More terms from _Hugo Pfoertner_, Oct 14 2007

%E a(37)-a(40) from _Hugo Pfoertner_, Jul 26 2019