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

1,2

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

Formula

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

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 *)

Prog

(Haskell)
import Data.List (findIndex)
import Data.Maybe (fromJust)
a220348 n = fromJust (findIndex (elem n) a183079_tabf) + 1
(Scheme, two variants)
(define (A220348 n) (+ 1 (A029837 (A220347 n))))
(define (A220348 n) (A070941 (+ -1 (A220347 n))))
;; Antti Karttunen, May 18 2015

Crossrefs

Cf. A029837, A070941, A183079, A220347.

Sequence in context: A129382 A353241 A163515 * A274010 A213711 A072649

Adjacent sequences: A220345 A220346 A220347 * A220349 A220350 A220351

Keyword

nonn

Author

Reinhard Zumkeller, Dec 12 2012

Extensions

Name edited by Michel Marcus, Jan 26 2022

Status

approved