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A186353 Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f and g are the odd numbers and the triangular numbers.  Complement of A186353. 5
1, 3, 6, 9, 12, 16, 21, 26, 31, 37, 44, 51, 58, 66, 75, 84, 93, 103, 114, 125, 136, 148, 161, 174, 187, 201, 216, 231, 246, 262, 279, 296, 313, 331, 350, 369, 388, 408, 429, 450, 471, 493, 516, 539, 562, 586, 611, 636, 661, 687, 714, 741, 768, 796, 825, 854, 883, 913, 944, 975, 1006, 1038, 1071, 1104, 1137, 1171, 1206, 1241, 1276, 1312, 1349, 1386, 1423, 1461, 1500, 1539, 1578, 1618, 1659, 1700, 1741, 1783, 1826, 1869, 1912, 1956, 2001, 2046, 2091 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..89.

FORMULA

a(n)=n+floor(-1/2+sqrt(4n-3/4))=A186352(n).

b(n)=n+floor((n^2+n+1)/4)=A186353(n).

EXAMPLE

First, write

1..3..5..7..9..11..13..15..17..21..23.. (odds)

1..3....6.....10.......15......21.... (triangular)

Then replace each number by its rank, where ties are settled by ranking the odd number after the triangular:

a=(2,4,5,7,8,10,11,13,14,15,....)=A186352

b=(1,3,6,9,12,16,21,26,31,37,...)=A186353.

MATHEMATICA

(See A186352.)

CROSSREFS

Cf. A186350, A186351, A186352.

Sequence in context: A260706 A194199 A072567 * A061796 A113241 A310153

Adjacent sequences:  A186350 A186351 A186352 * A186354 A186355 A186356

KEYWORD

nonn

AUTHOR

Clark Kimberling, Feb 18 2011

STATUS

approved

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Last modified February 17 17:59 EST 2020. Contains 331999 sequences. (Running on oeis4.)