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, 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

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