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.

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.

Links

Table of n, a(n) for n=1..87.

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

Cf. A186379, A186381, A186382.

Sequence in context: A129896 A134421 A092777 * A006463 A237886 A212555

Adjacent sequences: A186377 A186378 A186379 * A186381 A186382 A186383

Keyword

nonn

Author

Clark Kimberling, Feb 19 2011

Status

approved