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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

%I

%S 2,3,5,9,15,26,43,70,111,170,379,393,409,424,440,457,474,492,511,530,

%T 549,570,590,612,634,657,681,706,731,757,784,811,840,869,899,931,963,

%U 996,1030,1065,1101,1138,1177,1216,1257,1299,1342,1386,1431,1478,1526

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

%H Iain Fox, <a href="/A034073/b034073.txt">Table of n, a(n) for n = 0..10000</a>

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

%e a(20) = 549 -> 549^(1/8) = 2.{20}012088...;

%e a(21) = 570 -> 570^(1/8) = 2.{21}046863... and a(20)=549 < a(21)=570.

%e From _Jon E. Schoenfield_, Dec 09 2017: (Start)

%e n a(n) a(n)^(1/8)

%e -- ---- ---------------

%e 0 2 1.{0}9050773...

%e 1 3 1.{1}4720269...

%e 2 5 1.{2}2284454...

%e 3 9 1.{3}1607401...

%e 4 15 1.{4}0285055...

%e 5 26 1.{5}0269786...

%e 6 43 1.{6}0023423...

%e 7 70 1.{7}0073737...

%e 8 111 1.{8}0162903...

%e 9 170 1.{9}0022975...

%e 10 379 2.{10}053489...

%e 11 393 2.{11}008071...

%e 12 409 2.{12}063250...

%e ...

%e 99 6389 2.{99}005454...

%e 100 8529 3.{100}00407...

%e 101 8551 3.{101}00247... (End)

%o (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

%Y Cf. A034063, A034083.

%K nonn,base

%O 0,1

%A _Patrick De Geest_, Sep 15 1998

%E Name edited by _Jon E. Schoenfield_, Dec 09 2017

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Last modified October 24 11:27 EDT 2021. Contains 348225 sequences. (Running on oeis4.)