cp's OEIS Frontend

A123483 Second order Recamán's sequence: a(0) = 0; for n > 0, a(n) = a(n-1) - A005132(n) if that number is positive and not already in the sequence, otherwise a(n-1) + A005132(n).

%I A123483 #12 Feb 12 2024 08:40:08
%S A123483 0,1,4,10,8,15,2,22,34,13,24,46,36,59,50,26,18,43,86,148,106,169,128,
%T A123483 110,68,51,94,78,122,107,62,48,94,173,60,138,252,175,136,58,20,99,136,
%U A123483 56,92,11,46,128,162,79,112,28,60,145,114,200,170,83,54,142,170,81,108,198
%N A123483 Second order Recamán's sequence: a(0) = 0; for n > 0, a(n) = a(n-1) - A005132(n) if that number is positive and not already in the sequence, otherwise a(n-1) + A005132(n).
%C A123483 I conjecture that this sequence contains every natural number. (Even though through n=10000, we still haven't seen 3; we are still occasionally seeing small numbers.) This sequence has an interesting graph.
%C A123483 The smallest n such that a(n) = 3, 6, 12 are, respectively, 4729925, 5808155, 2093396. The following numbers less than 100 do not appear in the sequence for n <= 10^7: 7, 17, 19, 21, 23, 25, 27, 29, 35, 39, 41, 44, 45, 57, 61, 65, 67, 70, 71, 73, 77, 87, 91, 95. - _Nick Hobson_, Feb 18 2007
%H A123483 Franklin T. Adams-Watters, <a href="/A123483/b123483.txt">The first 10000 terms</a>
%H A123483 Nick Hobson, <a href="/A123483/a123483.py.txt">Python program for this sequence</a>
%Y A123483 Cf. A005132.
%K A123483 nonn
%O A123483 0,3
%A A123483 _Franklin T. Adams-Watters_, Sep 28 2006