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A279076
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Maximum starting value of X such that repeated replacement of X with X-ceiling(X/6) requires n steps to reach 0.
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5
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0, 1, 2, 3, 4, 5, 7, 9, 11, 14, 17, 21, 26, 32, 39, 47, 57, 69, 83, 100, 121, 146, 176, 212, 255, 307, 369, 443, 532, 639, 767, 921, 1106, 1328, 1594, 1913, 2296, 2756, 3308, 3970, 4765, 5719, 6863, 8236, 9884, 11861, 14234, 17081, 20498, 24598, 29518, 35422
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OFFSET
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0,3
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COMMENTS
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Limit_{n->oo} a(n)/(6/5)^n = 3.24387249751177521384734853905517802618171089570674...
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LINKS
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FORMULA
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a(n) = floor(a(n-1)*6/5) + 1.
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EXAMPLE
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7 -> 7-ceiling(7/6) = 5,
5 -> 5-ceiling(5/6) = 4,
4 -> 4-ceiling(4/6) = 3,
3 -> 3-ceiling(3/6) = 2,
2 -> 2-ceiling(2/6) = 1,
1 -> 1-ceiling(1/6) = 0,
so reaching 0 from 7 requires 6 steps;
8 -> 8-ceiling(8/6) = 6,
6 -> 6-ceiling(6/6) = 5,
5 -> 5-ceiling(5/6) = 4,
4 -> 4-ceiling(4/6) = 3,
3 -> 3-ceiling(3/6) = 2,
2 -> 2-ceiling(2/6) = 1,
1 -> 1-ceiling(1/6) = 0,
so reaching 0 from 8 (or more) requires 7 (or more) steps;
thus, 7 is the largest starting value from which 0 can be reached in 6 steps, so a(6) = 7.
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PROG
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(Magma) a:=[0]; aCurr:=0; for n in [1..51] do aCurr:=Floor(aCurr*6/5)+1; a[#a+1]:=aCurr; end for; a;
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CROSSREFS
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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), (this sequence) (k=6), A279077 (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, ...}?
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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