A034073 a(0)=2; a(n) is the smallest k > a(n-1) such that the fractional part of k^(1/8) starts with n.

2, 3, 5, 9, 15, 26, 43, 70, 111, 170, 379, 393, 409, 424, 440, 457, 474, 492, 511, 530, 549, 570, 590, 612, 634, 657, 681, 706, 731, 757, 784, 811, 840, 869, 899, 931, 963, 996, 1030, 1065, 1101, 1138, 1177, 1216, 1257, 1299, 1342, 1386, 1431, 1478, 1526

Offset

0,1

Links

Iain Fox, Table of n, a(n) for n = 0..10000

Formula

For n > 0, a(n) = ceiling((d + n/10^d)^8) where d = 1 + floor(log_10(n)). - Jon E. Schoenfield, Dec 09 2017

Example

a(20) = 549 -> 549^(1/8) = 2.{20}012088...;
a(21) = 570 -> 570^(1/8) = 2.{21}046863... and a(20)=549 < a(21)=570.
From Jon E. Schoenfield, Dec 09 2017: (Start)
    n  a(n)     a(n)^(1/8)
   --  ----  ---------------
    0     2  1.{0}9050773...
    1     3  1.{1}4720269...
    2     5  1.{2}2284454...
    3     9  1.{3}1607401...
    4    15  1.{4}0285055...
    5    26  1.{5}0269786...
    6    43  1.{6}0023423...
    7    70  1.{7}0073737...
    8   111  1.{8}0162903...
    9   170  1.{9}0022975...
   10   379  2.{10}053489...
   11   393  2.{11}008071...
   12   409  2.{12}063250...
...
   99  6389  2.{99}005454...
  100  8529  3.{100}00407...
  101  8551  3.{101}00247... (End)

Prog

(PARI) a(n) = if(n == 0, return(2)); my(d = 1 + logint(n, 10)); ceil((d + n/10^d)^8); \\ Iain Fox, Dec 09 2017

Crossrefs

Cf. A034063, A034083.

Sequence in context: A228646 A005517 A034063 * A114623 A079971 A355805

Adjacent sequences: A034070 A034071 A034072 * A034074 A034075 A034076

Keyword

nonn,base

Author

Patrick De Geest, Sep 15 1998

Extensions

Name edited by Jon E. Schoenfield, Dec 09 2017

Status

approved