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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.

%I A259935 #42 Feb 17 2025 12:14:42
%S A259935 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,
%T A259935 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,
%U A259935 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
%N A259935 Infinite sequence of positive integers such that a(n) = A000005(a(1) + a(2) + ... + a(n)) for all n >= 1.
%C A259935 V. S. Guba (2015) proved that such an infinite sequence exists. Numerical evidence suggests that it may also be unique (cf. A259934).
%C A259935 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
%H A259935 N. J. A. Sloane, <a href="/A259935/b259935.txt">Table of n, a(n) for n = 1..64800</a> (Based on Robert Israel's b-file for A259934.)
%H A259935 V. S. Guba et al., <a href="https://web.archive.org/web/20231210151810/http://math.hashcode.ru/questions/66579/%D1%82%D0%B5%D0%BE%D1%80%D0%B8%D1%8F-%D1%87%D0%B8%D1%81%D0%B5%D0%BB-%D0%BF%D0%BE%D1%81%D0%BB%D0%B5%D0%B4%D0%BE%D0%B2%D0%B0%D1%82%D0%B5%D0%BB%D1%8C%D0%BD%D0%BE%D1%81%D1%82%D1%8C-%D0%B8-%D0%B4%D0%B5%D0%BB%D0%B8%D1%82%D0%B5%D0%BB%D0%B8">Sequence and divisors</a>, 2015. (in Russian)
%F A259935 a(n) = A000005(A259934(n)) = A259934(n) - A259934(n-1).
%F A259935 gcd(a(n), A259934(n)) = A286540(n) = A009191(A259934(n)). - _Antti Karttunen_, Nov 26 2017
%Y A259935 First differences of A259934.
%Y A259935 Cf. A000005, A260257, A260085, A260123, A286540.
%K A259935 nonn,nice
%O A259935 1,1
%A A259935 _Max Alekseyev_, Jul 09 2015