A186347 Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f(i)=8i and g(j)=j^2. Complement of A186346.

1, 2, 4, 6, 8, 10, 13, 16, 19, 22, 26, 30, 34, 38, 43, 48, 53, 58, 64, 70, 76, 82, 89, 96, 103, 110, 118, 126, 134, 142, 151, 160, 169, 178, 188, 198, 208, 218, 229, 240, 251, 262, 274, 286, 298, 310, 323, 336, 349, 362, 376, 390, 404, 418, 433, 448, 463, 478, 494, 510, 526, 542, 559, 576, 593, 610, 628, 646, 664, 682, 701, 720, 739, 758, 778, 798, 818, 838, 859, 880, 901, 922, 944, 966, 988, 1010

Offset: 1

Author

Clark Kimberling, Feb 20 2011

Keywords

• nonn
• easy

Comments

a(n) = a(-8-n) for all n in Z using the formula. - Michael Somos, Apr 05 2024

Examples

			First, write
....8....16..24..32..40..48..56..64..72..80.. (8i)
1..4..9..16...25...36......49....64.......81 (squares)
Then replace each number by its rank, where ties are settled by ranking 8i before the square:
a=(3,5,7,9,11,12,14,15,17,..)=A186346
b=(1,2,4,6,8,10,13,16,19,...)=A186347.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (2,-1,0,1,-2,1).

Crossrefs

Cf. A186346, A186348, A186349.

Programs

Mathematica

(* See A186346. *)

PARI

a(n) = (n + 4)^2\8 - 2; \\ Michael Somos, Apr 05 2024

PARI

a(n)=n^2\8 + n \\ Charles R Greathouse IV, Apr 11 2024

Formula

a(n)=n+floor(sqrt(8n-1/2))=A186346(n).

b(n)=n+floor((n^2+1/2)/8)=A186347(n).

G.f.: x*(1 + x^2 - x^4)/((1 - x)^2 * (1 - x^4)). - Michael Somos, Apr 05 2024