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

1,2

Comments

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

Links

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

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, ...

Crossrefs

Cf. A037257, A035311, A073159, A073160.

Sequence in context: A021408 A011178 A136790 * A035311 A182310 A244591

Adjacent sequences: A073155 A073156 A073157 * A073159 A073160 A073161

Keyword

easy,nonn

Author

Paul D. Hanna, Jul 29 2002

Extensions

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

Status

approved