A259935 Infinite sequence of positive integers such that a(n) = A000005(a(1) + a(2) + ... + a(n)) for all n >= 1.

2, 4, 6, 6, 4, 8, 4, 8, 4, 8, 4, 4, 8, 8, 12, 4, 8, 4, 8, 4, 3, 4, 4, 15, 8, 10, 4, 8, 8, 8, 4, 16, 4, 8, 8, 6, 6, 8, 4, 16, 4, 8, 12, 4, 4, 8, 4, 16, 12, 4, 8, 4, 8, 8, 16, 4, 8, 8, 8, 8, 8, 8, 4, 16, 4, 8, 12, 8, 16, 12, 8, 16, 12, 4, 4, 8, 8, 8, 8, 8, 24, 8, 12, 8, 4, 8, 8, 8, 16, 8, 6, 6, 8, 4, 8, 4, 8, 8, 12, 8, 18, 8, 32, 24, 18, 4, 8, 16, 4, 16, 4, 8, 12, 8, 8, 8, 8, 8, 8, 12

Offset: 1

Author

Max Alekseyev, Jul 09 2015

Keywords

• nonn
• nice

Comments

V. S. Guba (2015) proved that such an infinite sequence exists. Numerical evidence suggests that it may also be unique (cf. A259934).

If there are infinitely many n with a(n) = a(n+1), then A175304 is infinite (see comment in A259934). - Vladimir Shevelev, Jul 21 2015

Links

• N. J. A. Sloane, Table of n, a(n) for n = 1..64800 (Based on Robert Israel's b-file for A259934.)
• V. S. Guba et al., Sequence and divisors, 2015. (in Russian)

Crossrefs

First differences of A259934.

Cf. A000005, A260257, A260085, A260123, A286540.

Formula

a(n) = A000005(A259934(n)) = A259934(n) - A259934(n-1).

gcd(a(n), A259934(n)) = A286540(n) = A009191(A259934(n)). - Antti Karttunen, Nov 26 2017