cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A178490 Primes of the form 2*p^k-1, where p is prime and k >= 1.

This page as a plain text file.
%I A178490 #12 Feb 21 2024 08:27:02
%S A178490 3,5,7,13,17,31,37,53,61,73,97,127,157,193,241,277,313,337,397,421,
%T A178490 457,541,577,613,661,673,733,757,877,997,1093,1153,1201,1213,1237,
%U A178490 1249,1321,1381,1453,1621,1657,1753,1873,1933,1993,2017,2137,2341,2473,2557,2593
%N A178490 Primes of the form 2*p^k-1, where p is prime and k >= 1.
%C A178490 Includes the Mersenne primes > 3 (A000668) and primes of the form 2p^2-1 (A092057) and 2p-1 (A005383) as subsequences; excluding the latter yields A178491.
%H A178490 Robert Israel, <a href="/A178490/b178490.txt">Table of n, a(n) for n = 1..10000</a>
%e A178490 a(1) = 7 = 2*2^2-1 and a(2) = 17 = 2*3^2-1 are also in A092057, and a(3) = 31 = 2*2^4-1 = A000668(3), but a(4) = 53 = 2*3^3-1 is in neither of these subsequences.
%p A178490 filter:= n -> isprime(n) and nops(numtheory:-factorset((n+1)/2))=1:
%p A178490 select(filter, [seq(i,i=3..10000,2)]); # _Robert Israel_, Feb 20 2024
%t A178490 Select[Prime[Range[20000]],Length[FactorInteger[(#+1)/2]]==1&]
%o A178490 (PARI) is_A178490(n) = isprime(n) & omega((n+1)\2)==1
%Y A178490 Cf. A000668, A005383, A092057, A178491.
%K A178490 nonn
%O A178490 1,1
%A A178490 _Farideh Firoozbakht_ and _M. F. Hasler_, Oct 09 2010