A382519 Odd positive integers m such that phi(m) and phi(m+1) are both powers of 2.

1, 3, 5, 15, 255, 65535, 4294967295

Offset

1,2

Comments

Sequence is finite with only 7 values. With the exception of m = 5, the others are products of the first k Fermat primes; i.e., products of A019434 and matching the initial terms of A051179. With the exception of m = 5, sequence resembles A250405.

Links

Table of n, a(n) for n=1..7.

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

Formula

a(n) = 2^2^k - 1 for k = 0, 1, 2, 3, 4, 5, equivalently the product of first k Fermat numbers, OR a(n) = 5. Sequence is finite because the next Fermat number, 4294967297 is composite.

Example

5 is present because phi(5) = 4 and phi(6) = 2, both powers of two.
15 is present because phi(15) = 8 and phi(16) = 8, both powers of two.
17 is not present because phi(17) = 16 but phi(18) = 6, not a power of two.

Crossrefs

Cf. A051179, A000215, A019434, A003401, A250405.

Subsequence of A382803.

Sequence in context: A374463 A175138 A248795 * A215444 A378176 A325257

Adjacent sequences: A382516 A382517 A382518 * A382520 A382521 A382522

Keyword

nonn,fini,full

Author

Caleb Stanford, Apr 05 2025

Status

approved