# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/

Search: id:a100035
Showing 1-1 of 1

%I A100035 #15 Aug 04 2020 15:32:06
%S A100035 1,2,3,1,4,3,5,4,2,5,1,6,5,7,6,4,7,3,6,2,7,1,8,7,9,8,6,9,5,8,4,9,3,8,
%T A100035 2,9,1,10,9,11,10,8,11,7,10,6,11,5,10,4,11,3,10,2,11,1,12,11,13,12,10,
%U A100035 13,9,12,8,13,7,12,6,13,5,12,4,13,3,12,2,13,1,14,13,15,14,12,15,11,14,10
%N A100035 a(n+1) occurs not earlier as a neighbor of terms = a(n): either it is the greatest number < a(n) or, if no such number exists, the smallest number > a(n); a(1) = 1.
%C A100035 The natural numbers (A000027) occur infinitely many times as disjoint subsequences, see the example below and A100036, A100037, A100038 and A100039: exactly one k exists for all x < y such that a(k) = x and (a(k-1) = y or a(k+1) = y).
%C A100035 a(2*k^2 + k + 1) = a(A084849(k)) = 1 for k >= 0;
%C A100035 a(2*k^2 - 3*k) = a(A014107(k)) = 2 for k > 1;
%C A100035 a(2*k^2 + 5*k) = a(A033537(k)) = 3 for k > 1;
%C A100035 a(2*k^2 + k - 5) = a(A100040(k)) = 4 for k > 2;
%C A100035 a(2*k^2 + k - 7) = a(A100041(k)) = 5 for k > 3.
%H A100035 Pontus von Brömssen, <a href="/A100035/b100035.txt">Table of n, a(n) for n = 1..10000</a>
%e A100035 First terms (10 = A, 11 = B, 12 = C) and some subsequences = A000027:
%e A100035 1231435425165764736271879869584938291A9BA8B7A6B5A4B3A2B1CBD
%e A100035 123.4.5....6.7........8.9............A.B................C.D.
%e A100035 ...1....2........3............4................5..........
%e A100035 ..........1........2............3................4......
%e A100035 .....................1............2................3....
%Y A100035 Cf. A000027, A014107, A033537, A100036, A100037, A100038, A100039, A100040, A100041.
%K A100035 nonn
%O A100035 1,2
%A A100035 _Reinhard Zumkeller_, Oct 31 2004

# Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE