A073160 -id:A073160 - cp's OEIS frontend

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

Paul D. Hanna, Jul 29 2002

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

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

Cf. A037257, A035311, A073159, A073160.

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, ...

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

A073159 Sums of adjacent terms of A073158. Together, A073158, A073159 and A073160 include all the positive integers uniquely.

Original entry on oeis.org

3, 6, 11, 12, 13, 18, 24, 29, 34, 35, 36, 41, 43, 48, 54, 55, 57, 62, 65, 70, 75, 78, 79, 83, 89, 92, 93, 95, 99, 101, 103, 108, 114, 117, 120, 121, 124, 130, 133, 139, 140, 141, 147, 150, 156, 161, 163, 167, 171, 173, 175, 178, 184, 190, 193, 195, 198, 205

Offset: 1

Paul D. Hanna, Jul 29 2002

a(n) is asymptotic to 7n/2.

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

Cf. A073158, A073160.

a(n) = A073158(n) + A073158(n-1), where A073158(0)=0.

a(34) onward corrected by Sean A. Irvine, Nov 19 2024

cp's OEIS Frontend

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.

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