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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

Table of n, a(n) for n=0..42.

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

Cf. A034066, A034086.

Sequence in context: A232165 A129955 A034066 * A272642 A241906 A079224

Adjacent sequences:  A034073 A034074 A034075 * A034077 A034078 A034079

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 May 27 12:27 EDT 2020. Contains 334657 sequences. (Running on oeis4.)