A073158 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.

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, 45, 47, 46, 49, 50, 51, 52, 56, 58, 59, 61, 60, 64, 66, 67, 72, 68, 73, 74, 76, 80, 81, 82, 85, 86, 87, 88, 90, 94, 96, 97, 98, 100, 105, 104, 106, 107, 110, 111, 113

Offset: 1

Author

Paul D. Hanna, Jul 29 2002

Keywords

• easy
• nonn

Comments

a(n)/n is asymptotic to 7n/4.

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A037257, A035311, A073159, A073160.

Formula

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, ...

Extensions

a(35) onward corrected by Sean A. Irvine, Nov 19 2024