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

1,2

Comments

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

Links

Table of n, a(n) for n=1..86.

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

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

Example

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.

Mathematica

(* See A186346. *)

Prog

(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

Crossrefs

Cf. A186346, A186348, A186349.

Sequence in context: A025224 A294023 A096182 * A302648 A269746 A056827

Adjacent sequences: A186344 A186345 A186346 * A186348 A186349 A186350

Keyword

nonn,easy

Author

Clark Kimberling, Feb 20 2011

Status

approved