A220348 Index of row where n occurs in A183079.

1, 2, 3, 3, 4, 4, 4, 5, 5, 4, 5, 6, 6, 5, 5, 6, 7, 7, 6, 6, 5, 7, 8, 8, 7, 7, 6, 5, 8, 9, 9, 8, 8, 7, 6, 6, 9, 10, 10, 9, 9, 8, 7, 7, 6, 10, 11, 11, 10, 10, 9, 8, 8, 7, 5, 11, 12, 12, 11, 11, 10, 9, 9, 8, 6, 6, 12, 13, 13, 12, 12, 11, 10, 10, 9, 7, 7, 7, 13

Offset: 1

Author

Reinhard Zumkeller, Dec 12 2012

Keywords

• nonn

Comments

A183079 seen as flattened sequence is a permutation of the natural numbers, therefore for each n there exists exactly 1 row in A183079 containing n.

In this sequence each n >= 2 occurs a total of 2^(n-2) times. - Antti Karttunen, May 18 2015

Links

• Reinhard Zumkeller (first 250 terms) & Antti Karttunen, Table of n, a(n) for n = 1..10440

Crossrefs

Cf. A029837, A070941, A183079, A220347.

Programs

Haskell

import Data.List (findIndex)
import Data.Maybe (fromJust)
a220348 n = fromJust (findIndex (elem n) a183079_tabf) + 1

Mathematica

(* b is A220347 *) b[n_] := b[n] = With[{r = (-1 + Sqrt[8n + 1])/2}, Which[n <= 1, n, IntegerQ[r], 2b[Floor[Sqrt[2n] + 1/2]] - 1, True, 2b[n - Floor[r]]]];
a[n_] := 1 + IntegerLength[b[n] - 1, 2];
Array[a, 100] (* Jean-François Alcover, Dec 05 2021 *)

Scheme

(define (A220348 n) (+ 1 (A029837 (A220347 n))))
;; Antti Karttunen, May 18 2015

Scheme

(define (A220348 n) (A070941 (+ -1 (A220347 n))))
;; Antti Karttunen, May 18 2015

Formula

a(n) = 1 + A029837(A220347(n)) = A070941(A220347(n)-1). - Antti Karttunen, May 18 2015

Extensions

Name edited by Michel Marcus, Jan 26 2022