A299535 Solutions to A000010(x) + A000010(x-1) = A000010(2*x).

2, 4, 16, 256, 496, 976, 2626, 3256, 3706, 5188, 11716, 13366, 18316, 22936, 25546, 46216, 49216, 49336, 57646, 65536, 164176, 184636, 198316, 215776, 286996, 307396, 319276, 388246, 397486, 415276, 491536, 568816, 589408, 686986, 840256, 914176, 952576, 983776

Offset: 1

Author

Benoit Cloitre, Feb 27 2018

Keywords

• nonn

Comments

All terms are even. Does lim_{n->oo} log(a(n))/log(n) exist?

Are all terms except 2 congruent to 4 (mod 6)? - Robert Israel, Feb 27 2018 [a(3710) = 3044760173456 is the next term after 2 that is congruent to 2 (mod 6). - Amiram Eldar, Jul 17 2022]

Includes the Fermat numbers 2^(2^j)+1 for j = 0..5, but no other terms of A019434. - Benoit Cloitre, corrected by Robert Israel, Mar 02 2018

Even numbers k for which A000010(k) = A000010(k-1). - Robert Israel, Mar 02 2018

Links

• Amiram Eldar, Table of n, a(n) for n = 1..5416 (calculated using the b-file at A001274; terms 1..100 from Robert Israel)
• Benoit Cloitre, Plot of log(a(n))/log(n+1) for n=1 up to 62

Crossrefs

Cf. A000010.

Programs

Magma

[n: n in [2..10^6] | EulerPhi(n)+EulerPhi(n-1) eq EulerPhi(2*n)]; // Bruno Berselli, Feb 27 2018

Maple

select(t -> numtheory:-phi(t)+ numtheory:-phi(t-1)=numtheory:-phi(2*t), [seq(i,i=2..10^6,2)]); # Robert Israel, Feb 27 2018

PARI

for(n=2, 200000, if(eulerphi(n) + eulerphi(n-1) == eulerphi(2*n), print1(n, ",")))

Extensions

More terms from Robert Israel, Feb 27 2018