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A034076 a(0)=2; a(n) is the smallest k > a(n-1) such that the fractional part of k^(1/11) starts with n. 2
2, 3, 8, 18, 41, 87, 176, 343, 643, 1165, 3503, 3691, 3888, 4095, 4311, 4538, 4776, 5025, 5285, 5558, 5844, 6143, 6455, 6782, 7125, 7482, 7856, 8247, 8656, 9083, 9529, 9994, 10481, 10988, 11518, 12072, 12649, 13251, 13879, 14534, 15217, 15929, 16672 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
FORMULA
For n > 0, a(n) = ceiling((d + n/10^d)^11) where d = 1 + floor(log_10(n)). - Jon E. Schoenfield, Nov 28 2017
EXAMPLE
a(4) = 41 -> 41^(1/11) = 1.{4}01576...;
a(5) = 87 -> 87^(1/11) = 1.{5}0079001... and a(4)=41 < a(5)=87.
From Jon E. Schoenfield, Nov 28 2017: (Start)
n a(n) a(n)^(1/11)
-- ------ ---------------
0 2 1.{0}6504108...
1 3 1.{1}1612317...
2 8 1.{2}1481404...
3 18 1.{3}0051594...
4 41 1.{4}0157620...
5 87 1.{5}0079001...
6 176 1.{6}0006459...
7 343 1.{7}0012668...
8 643 1.{8}0008041...
9 1165 1.{9}0001444...
10 3503 2.{10}001226...
11 3691 2.{11}001635...
12 3888 2.{12}001410...
...
99 170759 2.{99}000033...
100 254085 3.{100}00025...
101 254988 3.{101}00020... (End)
MATHEMATICA
fps[n_, i_]:=Module[{c=RealDigits[Surd[n, 11], 10, 10]}, FromDigits[ Take[ Drop[ c[[1]], c[[2]]], IntegerLength[i]]]]; nxt[{i_, n_}]:={i+1, Module[ {x=n+1}, While[fps[x, i+1]!=i+1, x++]; x]}; Transpose[NestList[nxt, {0, 2}, 50]][[2]] (* Harvey P. Dale, Nov 14 2013 *)
CROSSREFS
Sequence in context: A232165 A129955 A034066 * A272642 A241906 A079224
KEYWORD
nonn,base
AUTHOR
Patrick De Geest, Sep 15 1998
EXTENSIONS
Name edited by Jon E. Schoenfield, Nov 28 2017
STATUS
approved

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Last modified March 29 05:28 EDT 2024. Contains 371264 sequences. (Running on oeis4.)