A265332 - OEIS

A265332

a(n) is the index of the column in A265901 where n appears; also the index of the row in A265903 where n appears.

1, 2, 1, 3, 1, 1, 2, 4, 1, 1, 1, 2, 1, 2, 3, 5, 1, 1, 1, 1, 2, 1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 6, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 2, 3, 1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 5, 7, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 2, 3, 1, 1, 1, 2, 1, 1, 2, 1, 2, 3, 1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4

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OFFSET

1,2

COMMENTS

If all 1's are deleted, the remaining terms are the sequence incremented. - after Franklin T. Adams-Watters Oct 05 2006 comment in A051135.

Ordinal transform of A162598.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..8192

T. Kubo and R. Vakil, On Conway's recursive sequence, Discr. Math. 152 (1996), 225-252.

FORMULA

a(1) = 1; for n > 1, a(n) = A051135(n).

EXAMPLE

Illustration how the sequence can be constructed by concatenating the frequency counts Q_n of each successive level n of A004001-tree:

1 Q_0 = (1)

_2__ Q_1 = (2)

/ \

_3 __4_____ Q_2 = (1,3)

/ / | \

_5 _6 _7 __8___________ Q_3 = (1,1,2,4)

/ / / | / | \ \

_9 10 11 12 13 14 15___ 16_________ Q_4 = (1,1,1,2,1,2,3,5)

/ / / / | / / | |\ \ | \ \ \ \

17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

The above illustration copied from the page 229 of Kubo and Vakil paper (page 5 in PDF).

MATHEMATICA

terms = 120;

h[1] = 1; h[2] = 1;

h[n_] := h[n] = h[h[n - 1]] + h[n - h[n - 1]];

seq[nmax_] := seq[nmax] = (Length /@ Split[Sort @ Array[h, nmax, 2]])[[;; terms]];

seq[nmax = 2 terms];

seq[nmax += terms];

While[seq[nmax] != seq[nmax - terms], nmax += terms];

seq[nmax] (* Jean-François Alcover, Dec 19 2021 *)

PROG

(Scheme) (define (A265332 n) (if (= 1 n) 1 (A051135 n)))

CROSSREFS

Essentially same as A051135 apart from the initial term, which here is set as a(1)=1.

Cf. A004001, A265901, A265903.

Cf. A162598 (corresponding other index).

Cf. A265754.

Cf. also A267108, A267109, A267110.

Sequence in context: A123507 A188804 A122580 * A107041 A336812 A281426

Adjacent sequences: A265329 A265330 A265331 * A265333 A265334 A265335

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jan 09 2016

STATUS

approved