Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #10 Oct 20 2024 03:34:52
%S 3,7,31,127,8191,131071,524287,2147483647,137438953471,2199023255551,
%T 8796093022207,9007199254740991,2305843009213693951,
%U 147573952589676412927,9444732965739290427391,158456325028528675187087900671,2535301200456458802993406410751
%N Numbers of the form 2^p - 1, where p is a prime number that is not the sum, minus 1, of a Pythagorean triple.
%C See A136003 for the values of p.
%H Amiram Eldar, <a href="/A136005/b136005.txt">Table of n, a(n) for n = 1..236</a>
%F a(n) = 2^A136003(n) - 1.
%e a(3) = 31 because A136003(3) = 5 and 2^5 = 32 and 32-1 = 31.
%t 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 *)
%Y Cf. A000079, A000668, A136002, A136003.
%K nonn
%O 1,1
%A _Omar E. Pol_, Dec 17 2007
%E a(16)-a(17) from _Amiram Eldar_, Oct 20 2024