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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. 3
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 (list; graph; refs; listen; history; text; internal format)
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 A073031

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

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Last modified September 18 01:03 EDT 2021. Contains 347498 sequences. (Running on oeis4.)