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A259935 Infinite sequence of positive integers such that a(n) = A000005(a(1) + a(2) + ... + a(n)) for all n >= 1. 9
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Falcao (2015) proved that such an infinite sequence exists. Numerical evidence suggests that it may be also 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.)

Falcao et al., Sequence and divisors, 2015. (in Russian)

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

CROSSREFS

First differences of A259934.

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

Sequence in context: A248844 A257821 A238365 * A054584 A049041 A092337

Adjacent sequences:  A259932 A259933 A259934 * A259936 A259937 A259938

KEYWORD

nonn,nice

AUTHOR

Max Alekseyev, Jul 09 2015

STATUS

approved

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Last modified February 22 06:17 EST 2018. Contains 299430 sequences. (Running on oeis4.)