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%I #12 Mar 15 2018 18:28:44
%S 1,1,2,4,3,6,7,1,8,10,11,6,13,7,15,16,9,12,30,10,14,11,23,24,25,4,27,
%T 28,29,-11,31,16,22,34,21,36,37,19,39,40,41,42,43,44,45,23,47,8,49,25,
%U 51,52,53,27,34,-1,38,29,59,60,61,31,63,64,65,66,67,34,307,70,71
%N Start with positive integers (A000027), and at each step n >= 1 subtract from the term at position n + a(n) the value a(n).
%C The first 71 terms are correct if the following conjecture is true: n+a(n)<=0 or n+a(n)>71 for n >= 2^30.
%C The sequence of negative terms begins: -11, -1, -261, -11, -253, -319, -341, -407, -451, -528, -329, -371, -29, -31, -649, -619, -427, -737, -37, ...
%C Indices of negative terms: 30, 56, 330, 616, 690, 870, 930, 1110, 1230, 1288, 1410, 1590, 1624, 1736, 1770, 1820, 1830, 2010, 2072, ...
%C Numbers n such that a(n)=n: 1, 4, 6, 7, 10, 11, 13, 15, 16, 23, 24, 25, 27, 28, 29, 31, 34, 36, 37, 39, 40, 41, 42, 43, 44, 45, ...
%C The sequence of numbers n such that n+a(n)<0 begins: 1485264, 2029290, 6156150, 6872250, 8338512, 8769090, 10420410, 13448490, 16654110, 25894770, ...
%o (Python)
%o TOP = 2**30 # if enough RAM
%o a = [1]*TOP
%o for n in range(1,TOP):
%o a[n]=n
%o for n in range(1,TOP):
%o if n+a[n]<TOP and n+a[n]>0: a[n+a[n]] -= a[n]
%o for n in range(1,1000):
%o print str(a[n])+',',
%Y Cf. A000027, A136119, A137319, A137417, A137418, A137894.
%K sign
%O 1,3
%A _Alex Ratushnyak_, Nov 22 2013
%E Corrected by _Alex Ratushnyak_, Dec 28 2013
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