OFFSET
1,2
COMMENTS
Numbers m such that m and m+1 are in A003401
Each of m and m+1 must be a power of 2 times a product of Fermat primes.
Apart from term 5, odd terms are of the form 2^2^k - 1 for k in 0...5.
Even terms are exactly numbers of the form 2^2^k such that 2^2^k + 1 is a Fermat prime (A019434).
The sequence is thus infinite iff A019434 is infinite, i.e., iff there are infinitely many Fermat primes.
LINKS
User John and Caleb Stanford (Math StackExchange), A possible Property of Euler's totient function: n such that phi(n) and phi(n+1) are both powers of two
EXAMPLE
16 is present because phi(16) = 8 and phi(17) = 16, both powers of two.
17 is not present because phi(17) = 16 but phi(18) = 6, not a power of two.
CROSSREFS
KEYWORD
nonn,hard
AUTHOR
Caleb Stanford, Apr 05 2025
STATUS
approved
