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%I #9 Nov 19 2024 17:13:56
%S 1,2,4,7,5,8,10,14,15,19,16,20,21,22,26,28,27,30,32,33,37,38,40,39,44,
%T 45,47,46,49,50,51,52,56,58,59,61,60,64,66,67,72,68,73,74,76,80,81,82,
%U 85,86,87,88,90,94,96,97,98,100,105,104,106,107,110,111,113
%N a() = 1,2,4,7,... [ A073158 ], adjacent sums = 3,6,11... [ A073159 ] and 2nd adjacent sums = 9,17,... [ A073160 ] are disjoint but not monotonic; adjoin next free number to A073158 to construct three sequences that together include all positive integers.
%C a(n)/n is asymptotic to 7n/4.
%H Sean A. Irvine, <a href="/A073158/b073158.txt">Table of n, a(n) for n = 1..1000</a>
%F A073158:_1, 2, 4, 7, 5, 8, 10, 14, 15, 19, 16, 20, 21, 22, 26, 28, 27, ... A073159:__3, 6, 11, 12, 13, 18, 24, 29, 34, 35, 36, 41, 43, 48, 54, 55, ... A073160:___9, 17, 23, 25, 31, 42, 53, 63, 69, 71, 77, 84, 91, 102, 109, ...
%Y Cf. A037257, A035311, A073159, A073160.
%K easy,nonn
%O 1,2
%A _Paul D. Hanna_, Jul 29 2002
%E a(35) onward corrected by _Sean A. Irvine_, Nov 19 2024