A034074 a(0)=2; a(n) is the smallest k > a(n-1) such that the fractional part of k^(1/9) starts with n.

2, 3, 6, 11, 21, 39, 69, 119, 199, 323, 795, 829, 866, 903, 942, 982, 1024, 1067, 1113, 1159, 1208, 1258, 1310, 1364, 1420, 1478, 1539, 1601, 1665, 1732, 1802, 1873, 1948, 2024, 2104, 2186, 2271, 2360, 2451, 2545, 2642, 2743, 2847, 2955, 3066, 3181, 3300

Offset

0,1

Links

Table of n, a(n) for n=0..46.

Formula

For n > 0, a(n) = ceiling((d + n/10^d)^9) where d = 1 + floor(log_10(n)). - Jon E. Schoenfield, Dec 09 2017

Example

   a(9) = 323 -> 323^(1/9) = 1.{9}0020422...;
  a(10) = 795 -> 795^(1/9) = 2.{10}021141... and a(9)=323 < a(10)=795.
From Jon E. Schoenfield, Dec 09 2017: (Start)
    n   a(n)     a(n)^(1/9)
   --  ------  ---------------
    0       2  1.{0}8005973...
    1       3  1.{1}2983096...
    2       6  1.{2}2028493...
    3      11  1.{3}0529988...
    4      21  1.{4}0253353...
    5      39  1.{5}0239786...
    6      69  1.{6}0072440...
    7     119  1.{7}0065542...
    8     199  1.{8}0064508...
    9     323  1.{9}0020422...
   10     795  2.{10}021141...
   11     829  2.{11}000671...
   12     866  2.{12}026857...
...
   99   19101  2.{99}001178...
  100   26440  3.{100}00492...
  101   26517  3.{101}00673... (End)

Crossrefs

Cf. A034064, A034084.

Sequence in context: A246699 A079969 A034064 * A018175 A316356 A049856

Adjacent sequences: A034071 A034072 A034073 * A034075 A034076 A034077

Keyword

nonn,base

Author

Patrick De Geest, Sep 15 1998

Extensions

Name edited by Jon E. Schoenfield, Dec 09 2017

Status

approved