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A279077 Maximum starting value of X such that repeated replacement of X with X-ceiling(X/7) requires n steps to reach 0. 5
0, 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 18, 22, 26, 31, 37, 44, 52, 61, 72, 85, 100, 117, 137, 160, 187, 219, 256, 299, 349, 408, 477, 557, 650, 759, 886, 1034, 1207, 1409, 1644, 1919, 2239, 2613, 3049, 3558, 4152, 4845, 5653, 6596, 7696, 8979, 10476, 12223, 14261 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Inspired by A278586.

Lim_{n->inf} a(n)/(7/6)^n = 4.03710211215303193642791458111196922950551168987041...

LINKS

Table of n, a(n) for n=0..53.

FORMULA

a(n) = floor(a(n-1)*7/6) + 1.

EXAMPLE

  10 -> 10-ceiling(10/7) = 8,

   8 ->  8-ceiling(8/7)  = 6,

   6 ->  6-ceiling(6/7)  = 5,

   5 ->  5-ceiling(5/7)  = 4,

   4 ->  4-ceiling(4/7)  = 3,

   3 ->  3-ceiling(3/7)  = 2,

   2 ->  2-ceiling(2/7)  = 1,

   1 ->  1-ceiling(1/7)  = 0,

so reaching 0 from 10 requires 8 steps;

  11 -> 11-ceiling(11/7) = 9,

   9 ->  9-ceiling(9/7)  = 7,

   7 ->  7-ceiling(7/7)  = 6,

   6 ->  6-ceiling(6/7)  = 5,

   5 ->  5-ceiling(5/7)  = 4,

   4 ->  4-ceiling(4/7)  = 3,

   3 ->  3-ceiling(3/7)  = 2,

   2 ->  2-ceiling(2/7)  = 1,

   1 ->  1-ceiling(1/7)  = 0,

so reaching 0 from 11 (or more) requires 9 (or more) steps;

thus, 10 is the largest starting value from which 0 can be reached in 8 steps, so a(8) = 10.

PROG

(MAGMA) a:=[0]; aCurr:=0; for n in [1..53] do aCurr:=Floor(aCurr*7/6)+1; a[#a+1]:=aCurr; end for; a;

CROSSREFS

Cf. A278586.

See the following sequences for maximum starting value of X such that repeated replacement of X with X-ceiling(X/k) requires n steps to reach 0: A000225 (k=2), A006999 (k=3), A155167 (k=4, apparently; see Formula entry there), A279075 (k=5), A279076 (k=6), (this sequence) (k=7), A279078 (k=8), A279079 (k=9), A279080 (k=10). For each of these values of k, is the sequence the L-sieve transform of {k-1, 2k-1, 3k-1, ...}?

Sequence in context: A033058 A060470 A003044 * A018541 A018293 A015702

Adjacent sequences:  A279074 A279075 A279076 * A279078 A279079 A279080

KEYWORD

nonn

AUTHOR

Jon E. Schoenfield, Dec 06 2016

STATUS

approved

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Last modified September 18 11:20 EDT 2021. Contains 347518 sequences. (Running on oeis4.)