A186220 Adjusted joint rank sequence of (g(i)) and (f(j)) with f(i) before g(j) when f(i)=g(j), where f and g are the triangular numbers and squares. Complement of A186219.
2, 4, 6, 9, 11, 14, 16, 18, 21, 23, 26, 28, 30, 33, 35, 38, 40, 42, 45, 47, 50, 52, 55, 57, 59, 62, 64, 67, 69, 71, 74, 76, 79, 81, 84, 86, 88, 91, 93, 96, 98, 100, 103, 105, 108, 110, 112, 115, 117, 120, 122, 125, 127, 129, 132, 134, 137, 139, 141, 144, 146, 149, 151, 154, 156, 158, 161, 163, 166, 168, 170, 173, 175, 178, 180, 182, 185, 187, 190, 192, 195, 197, 199, 202, 204, 207, 209, 211, 214, 216, 219, 221, 224, 226, 228, 231, 233, 236, 238, 240
Offset: 1
Keywords
Examples
First, write 1..3...6..10..15...21..28..36..45... (triangular) 1....4.. 9......16...25....36....49.. (square) Replace each number by its rank, where ties are settled by ranking the triangular number before the square: a=(1,3,5,7,8,10,12,13,...) = A186219; b=(2,4,6,9,11,14,16,18,...) = A186220.
Links
- G. C. Greubel, Table of n, a(n) for n = 1..10000
Programs
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Magma
[n + Floor((-1 + Sqrt(8*n^2 + 3))/2): n in [1..100]]; // G. C. Greubel, Aug 26 2018
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Mathematica
(See A186219.) Table[n + Floor[(-1 + Sqrt[8*n^2 + 3])/2], {n, 1, 100}] (* G. C. Greubel, Aug 26 2018 *)
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PARI
vector(100, n, n + floor((-1 + sqrt(8*n^2 + 3))/2)) \\ G. C. Greubel, Aug 26 2018
Formula
See A186219.
Comments