A136005 Numbers of the form 2^p - 1, where p is a prime number that is not the sum, minus 1, of a Pythagorean triple.

3, 7, 31, 127, 8191, 131071, 524287, 2147483647, 137438953471, 2199023255551, 8796093022207, 9007199254740991, 2305843009213693951, 147573952589676412927, 9444732965739290427391, 158456325028528675187087900671, 2535301200456458802993406410751

Offset

1,1

Comments

See A136003 for the values of p.

Links

Amiram Eldar, Table of n, a(n) for n = 1..236

Formula

a(n) = 2^A136003(n) - 1.

Example

a(3) = 31 because A136003(3) = 5 and 2^5 = 32 and 32-1 = 31.

Mathematica

q[n_] := PrimeQ[n] && (n == 2 || Module[{d = Divisors[(n+1)/2]}, AllTrue[Range[3, Length[d]], d[[#]] >= 2 * d[[#-1]] &]]); 2^Select[Range[100], q] - 1 (* Amiram Eldar, Oct 20 2024 *)

Crossrefs

Cf. A000079, A000668, A136002, A136003.

Sequence in context: A093535 A081093 A057612 * A336720 A183077 A088552

Adjacent sequences: A136002 A136003 A136004 * A136006 A136007 A136008

Keyword

nonn

Author

Omar E. Pol, Dec 17 2007

Extensions

a(16)-a(17) from Amiram Eldar, Oct 20 2024

Status

approved