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

Author

Clark Kimberling, Feb 19 2011

Keywords

• nonn

Comments

See A186379.

Examples

			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.
		

Crossrefs

Cf. A186379, A186381, A186382.

Programs

Mathematica

(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).