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A186380
Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f(i)=4i and g(j)=j(j+1)/2 (triangular number). Complement of A186379.
4
1, 2, 4, 6, 8, 11, 14, 17, 20, 23, 27, 31, 35, 40, 45, 50, 55, 60, 66, 72, 78, 85, 92, 99, 106, 113, 121, 129, 137, 146, 155, 164, 173, 182, 192, 202, 212, 223, 234, 245, 256, 267, 279, 291, 303, 316, 329, 342, 355, 368, 382, 396, 410, 425, 440, 455, 470, 485, 501, 517, 533, 550, 567, 584, 601, 618, 636, 654, 672, 691, 710, 729, 748, 767, 787, 807, 827, 848, 869, 890, 911, 932, 954, 976, 998, 1021, 1044
OFFSET
1,2
COMMENTS
See A186379.
FORMULA
a(n)=n+floor(-1/2+sqrt(8n-3/4))=A186379(n).
b(n)=n+floor((n^2+n+1)/8)=A186380(n).
EXAMPLE
First, write
.....4..8..12..16..20..24..28.. (4*i)
1..3..6..10..15.....21.....28.. (triangular)
Then replace each number by its rank, where ties are settled by ranking 4i before the triangular:
a=(3,5,7,9,10,12,13,15,16,..)=A186379
b=(1,2,4,6,8,11,14,17,20,...)=A186380.
MATHEMATICA
(See A186379.)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Feb 19 2011
STATUS
approved