A072347 -id:A072347

Search: a072347 -id:a072347

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A272530

Position of first occurrence of n in A072347.

+20
2

0, 3, 7, 27, 15, 427, 55, 31, 215, 219, 111, 119, 63, 431, 443, 471, 439, 223, 239, 1879, 127, 1719, 863, 1755, 891, 887, 879, 3423, 447, 495, 479, 3451, 3447, 255, 3439, 3503, 1727, 27355, 1967, 1787, 1775, 14167, 1783, 1759, 1911, 1903, 895, 7855, 991, 959, 6907, 6895, 7087, 55983, 511, 7099, 6879, 14043, 7007, 3455

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

a(n) == 3 (mod 4) for n > 1, since A072347(2k) = A072347(floor(k/2)) and A072347(4k+1) = A072347(2k+1). - Robert Israel, May 04 2016

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 3341 terms from Robert Israel)

Rémy Sigrist, Colored logarithmic scatterplot of a(n) for n = 1..10000 (where the color is function of the Hamming weight of a(n))

MAPLE

# using procedure a from A072347

R[1]:= 0:

for n from 3 to 100000 by 4 do

v:= a(n);

if not assigned(R[v]) then R[v]:= n

od:

for n from 1 while assigned(R[n]) do od:

seq(R[i], i=1..n-1); # Robert Israel, May 04 2016

MATHEMATICA

Block[{c, s}, c[w_] := With[{n = Length@ w}, Which[n == 0, 1, n == 1, First@ w, True, Last[w] c[Most@ w] + c[Most@ Most@ w]]]; s = {1}~Join~Array[c[IntegerDigits[#, 2]] &, 10^4]; TakeWhile[Array[-1 + FirstPosition[s, #][[1]] &, 50], IntegerQ]] (* Michael De Vlieger, Jan 20 2018, after Jean-François Alcover at A072347 *)

CROSSREFS

Cf. A072347.

KEYWORD

nonn,look

AUTHOR

Jeffrey Shallit, May 02 2016

STATUS

approved

A227992

Numbers m such that the continuants of their binary representations defined in A072347 equal 1.

+20
1

0, 1, 2, 4, 6, 8, 10, 16, 18, 24, 26, 32, 34, 40, 42, 64, 66, 72, 74, 96, 98, 104, 106, 128, 130, 136, 138, 160, 162, 168, 170, 256, 258, 264, 266, 288, 290, 296, 298, 384, 386, 392, 394, 416, 418, 424, 426, 512, 514, 520, 522, 544, 546, 552, 554, 640, 642, 648

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Aug 05 2013

STATUS

approved

A073300

If n=pqr...st in ternary, a(n)=value of the continuant [p,q,r,...,s,t].

+10
2

1, 1, 2, 1, 2, 3, 1, 3, 5, 1, 2, 3, 1, 3, 5, 1, 4, 7, 2, 3, 4, 2, 5, 8, 2, 7, 12, 1, 2, 3, 1, 3, 5, 1, 4, 7, 2, 3, 4, 2, 5, 8, 2, 7, 12, 3, 4, 5, 3, 7, 11, 3, 10, 17, 1, 3, 5, 1, 4, 7, 1, 5, 9, 3, 5, 7, 3, 8, 13, 3, 11, 19, 5, 7, 9, 5, 12, 19, 5, 17, 29, 1, 2, 3, 1, 3, 5, 1, 4, 7, 2, 3, 4, 2, 5, 8, 2, 7

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

COMMENTS

The continuant function is defined in A072347. The successive record values in this sequence occur at n=0,2,5,8 and, for k>=3, at n=3^k-3^(k-1)-1, 3^k-3^(k-2)-1 and 3^k-1 and are given in A073301.

a(3^n-1) = A000129(n+1) for n>=0. - Alois P. Heinz, Aug 06 2013

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..6560 (6560 = 3^8-1)

Wikipedia, Continuant

MAPLE

c:= proc() option remember;

if nargs=0 then 1

elif nargs=1 then args[1]

else args[-1]*c(seq(args[i], i=1..nargs-1))

+c(seq(args[i], i=1..nargs-2))

end:

a:= n-> `if`(n=0, 1, c(convert(n, base, 3)[])):

seq(a(n), n=0..120); # Alois P. Heinz, Aug 06 2013

CROSSREFS

Cf. A072347.

KEYWORD

base,nonn,look

AUTHOR

John W. Layman, Jul 23 2002

STATUS

approved

A073301

a(n) is the n-th new record value in A073300.

+10
2

1, 2, 3, 5, 7, 8, 12, 17, 19, 29, 41, 46, 70, 99, 111, 169, 239, 268, 408, 577, 647, 985, 1393, 1562, 2378, 3363, 3771, 5741, 8119, 9104, 13860, 19601, 21979, 33461, 47321, 53062, 80782, 114243, 128103, 195025, 275807, 309268, 470832, 665857, 746639

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Nathaniel Johnston, Table of n, a(n) for n = 1..2500

FORMULA

For n>=7, a(3n)=a(3n-2)+a(3n-4), a(3n+1)=a(3n-1)+a(3n-2) and a(3n+2)=a(3n+1)+a(3n-2). - R. J. Mathar, Jun 27 2007

MAPLE

A073301 := proc(n) option remember: local f6: f6:=[1, 2, 3, 5, 7, 8]: if(n<=6)then return f6[n]: elif(n mod 3 = 0)then return procname(n-2)+procname(n-4): elif(n mod 3 = 1)then return procname(n-2)+procname(n-3): else return procname(n-1)+procname(n-4): fi: end: seq(A073301(n), n=1..50); # Nathaniel Johnston, May 01 2011

CROSSREFS

Cf. A073300, A072347.

KEYWORD

base,nonn,easy

AUTHOR

John W. Layman, Jul 23 2002

EXTENSIONS

Corrected by T. D. Noe, Oct 25 2006

STATUS

approved

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