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 A382803 #41 Apr 18 2025 21:29:29 %S A382803 1,2,3,4,5,15,16,255,256,65535,65536,4294967295 %N A382803 Positive integers m such that phi(m) and phi(m+1) are both powers of 2. %C A382803 Numbers m such that m and m+1 are in A003401 %C A382803 Each of m and m+1 must be a power of 2 times a product of Fermat primes. %C A382803 Apart from term 5, odd terms are of the form 2^2^k - 1 for k in 0...5. %C A382803 Even terms are exactly numbers of the form 2^2^k such that 2^2^k + 1 is a Fermat prime (A019434). %C A382803 The sequence is thus infinite iff A019434 is infinite, i.e., iff there are infinitely many Fermat primes. %H A382803 User John and Caleb Stanford (Math StackExchange), <a href="https://math.stackexchange.com/questions/1886835">A possible Property of Euler's totient function: n such that phi(n) and phi(n+1) are both powers of two</a> %e A382803 16 is present because phi(16) = 8 and phi(17) = 16, both powers of two. %e A382803 17 is not present because phi(17) = 16 but phi(18) = 6, not a power of two. %Y A382803 Cf. A000010, A000215, A003401, A019434, A051179, A382519 (odd terms). %K A382803 nonn,hard %O A382803 1,2 %A A382803 _Caleb Stanford_, Apr 05 2025