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.
%I A074781 #44 Oct 26 2024 10:29:59
%S A074781 3,5,7,11,13,17,23,29,41,47,53,59,83,89,97,107,113,137,149,167,173,
%T A074781 179,193,227,233,257,263,269,293,317,347,353,359,383,389,449,467,479,
%U A074781 503,509,557,563,569,587,593,641,653,719,769,773,797,809,839,857,863,887
%N A074781 Primes of the form p*2^k + 1 for any k and any prime p.
%C A074781 From _Bernard Schott_, Dec 14 2020: (Start)
%C A074781 Equivalently, primes p such that the ratio (p-1)/gpf(p-1) = 2^k where gpf(m) is the greatest prime factor of m, A006530.
%C A074781 Paul Erdős asked if there are infinitely many primes p in this sequence (see R. K. Guy reference). (End)
%D A074781 Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, Section B46, p. 154.
%H A074781 T. D. Noe, <a href="/A074781/b074781.txt">Table of n, a(n) for n = 1..2000</a>
%H A074781 Graeme L. Cohen, <a href="https://eudml.org/doc/210499">On a conjecture of Makowski and Schinzel</a>, Colloquium Mathematicae, Vol. 74, No. 1 (1997), pp. 1-8.
%e A074781 3 = 2*2^0+1 is a term and 2/2 = 1 = 2^0.
%e A074781 7 = 3*2^1+1 is a term and 6/3 = 2 = 2^1.
%e A074781 13 = 3*2^2+1 is a term and 12/3 = 4 = 2^2.
%e A074781 41 = 5*2^3+1 is a term and 40/5 = 8 = 2^3.
%e A074781 113 = 7*2^4+1 is a term and 112/7 = 16 = 2^4.
%p A074781 alias(pf = NumberTheory:-PrimeFactors): gpf := n -> max(pf(n)):
%p A074781 is_a := n -> isprime(n) and pf((n-1)/gpf(n-1)) = {2}:
%p A074781 3, op(select(is_a, [$3..919])); # _Peter Luschny_, Dec 14 2020
%t A074781 Select[Range[3, 1000], PrimeQ[#] && !CompositeQ[(# - 1)/2^IntegerExponent[(# - 1), 2]] &] (* _Amiram Eldar_, Dec 28 2018 *)
%Y A074781 Cf. A000079, A006093, A006530, A052126, A339464.
%Y A074781 Cf. other ratios : A339463, A339465, A339466.
%Y A074781 Subsequences: A039687, A051900, A058500 (this sequence without the Fermat primes), A090866, A147545,
%K A074781 nonn
%O A074781 1,1
%A A074781 Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Sep 07 2002