A376337 Numbers k such that phi(k)/2 + 1 = phi(k + 1) where phi = A000010.

3, 7, 9, 31, 127, 8191, 131071, 524287, 2147483647

Offset

1,1

Comments

Conjecture: this sequence is the union {9} and the Mersenne primes A000668.

a(10) > 1.2 * 10^15.

Links

Table of n, a(n) for n=1..9.

Example

Number 9 is in this sequence because phi(9)/2 + 1 = 6/2 + 1 = 3 + 1 = 4 is equal to phi(9 + 1) = phi(10) = 4.

Mathematica

Select[Range[550000], EulerPhi[#]/2+1==EulerPhi[#+1] &] (* Stefano Spezia, Sep 22 2024 *)

Prog

(Magma) [k: k in [3..5*10^6] | ((EulerPhi(k) div 2) + 1) eq EulerPhi(k + 1)];

Crossrefs

Cf. A000010, A000668, A191611, A376338.

Sequence in context: A246659 A072087 A328462 * A328233 A031161 A031882

Adjacent sequences: A376334 A376335 A376336 * A376338 A376339 A376340

Keyword

nonn,more

Author

Juri-Stepan Gerasimov, Sep 20 2024

Extensions

a(9) from Jud McCranie, Jan 20 2026

Status

approved