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.

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

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 * A362032 A061796 A113241

Adjacent sequences: A186350 A186351 A186352 * A186354 A186355 A186356

Keyword

nonn

Author

Clark Kimberling, Feb 18 2011

Status

approved