A248346 Primes of the form 2^x - y^2, with y^2 < 2^x.

2, 3, 7, 23, 31, 47, 71, 79, 103, 127, 151, 199, 223, 271, 367, 431, 463, 487, 503, 727, 751, 823, 967, 1087, 1303, 1319, 1423, 1439, 1559, 1607, 1759, 1823, 1879, 1951, 1999, 2039, 2143, 3343, 3527, 3623, 3967, 4447, 4943, 5167, 5503, 5591, 5791, 6199, 6343

Offset

1,1

Comments

Primes in A051213.

Links

Table of n, a(n) for n=1..49.

Example

7 is in this sequence because 7 = 2^3 - 1^2 = 2^4 - 3^2 = 2^5 - 5^2 = 2^7 - 11^2 = 2^15 - 181^2.
1559 is in this sequence because 1559 = 2^19 - 723^2 is prime. - Sean A. Irvine, Apr 28 2022

Mathematica

Select[Union[Flatten[Table[2^x - y^2, {x, 16}, {y, 0, Floor[Sqrt[2^x]]}]]], PrimeQ] (* Alonso del Arte, Oct 05 2014 *)

Crossrefs

Cf. A038198, A051213, A060728, A248344.

Primes in A056007 form a subset of the numbers in this sequence.

Sequence in context: A120302 A093363 A291525 * A236514 A211997 A127581

Adjacent sequences: A248343 A248344 A248345 * A248347 A248348 A248349

Keyword

nonn

Author

Juri-Stepan Gerasimov, Oct 05 2014

Extensions

a(24)-a(38) from Alonso del Arte, Oct 05 2014

More terms and missing terms inserted by Sean A. Irvine, Apr 28 2022

Status

approved