A034075 a(0)=2; a(n) is the smallest k > a(n-1) such that the fractional part of k^(1/10) starts with n.

2, 3, 7, 14, 29, 58, 110, 202, 358, 614, 1668, 1750, 1834, 1923, 2015, 2111, 2211, 2316, 2425, 2538, 2656, 2780, 2908, 3042, 3181, 3326, 3477, 3633, 3797, 3967, 4143, 4327, 4518, 4716, 4923, 5137, 5360, 5591, 5832, 6082, 6341, 6610, 6889, 7179, 7480

Offset

0,1

Links

Table of n, a(n) for n=0..44.

Formula

For n > 0, a(n) = ceiling((d + n/10^d)^10) where d = 1 + floor(log_10(n)). - Jon E. Schoenfield, Nov 26 2017

Example

a(7)=202 -> 202^(1/10) = 1.{7}0033751...;
a(8)=358 -> 358^(1/10) = 1.{8}0048000... and a(7)=202 < a(8)=358.
From Jon E. Schoenfield, Nov 26 2017: (Start)
    n   a(n)    a(n)^(1/10)
   --  -----  ---------------
    0      2  1.{0}7177346...
    1      3  1.{1}1612317...
    2      7  1.{2}1481404...
    3     14  1.{3}0200545...
    4     29  1.{4}0036033...
    5     58  1.{5}0086904...
    6    110  1.{6}0007105...
    7    202  1.{7}0033751...
    8    358  1.{8}0048000...
    9    614  1.{9}0027667...
   10   1668  2.{10}000149...
   11   1750  2.{11}010372...
   12   1834  2.{12}001987...
...
   99  57110  2.{99}000019...
  100  81963  3.{100}00064...
  101  82228  3.{101}00147... (End)

Crossrefs

Cf. A034065, A034085.

Sequence in context: A131666 A135258 A034065 * A281716 A192570 A019595

Adjacent sequences: A034072 A034073 A034074 * A034076 A034077 A034078

Keyword

nonn,base

Author

Patrick De Geest, Sep 15 1998

Extensions

Name edited by Jon E. Schoenfield, Nov 26 2017

Status

approved