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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. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
See A186219.
LINKS
FORMULA
See A186219.
EXAMPLE
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.
MATHEMATICA
(See A186219.)
Table[n + Floor[(-1 + Sqrt[8*n^2 + 3])/2], {n, 1, 100}] (* G. C. Greubel, Aug 26 2018 *)
PROG
(PARI) vector(100, n, n + floor((-1 + sqrt(8*n^2 + 3))/2)) \\ G. C. Greubel, Aug 26 2018
(Magma) [n + Floor((-1 + Sqrt(8*n^2 + 3))/2): n in [1..100]]; // G. C. Greubel, Aug 26 2018
CROSSREFS
Sequence in context: A203988 A160813 A247515 * A285075 A186316 A265286
KEYWORD
nonn
AUTHOR
Clark Kimberling, Feb 15 2011
STATUS
approved

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Last modified June 16 19:52 EDT 2024. Contains 373432 sequences. (Running on oeis4.)