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A034073
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a(0)=2; a(n) is the smallest k > a(n-1) such that the fractional part of k^(1/8) starts with n.
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3
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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
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OFFSET
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0,1
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LINKS
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FORMULA
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For n > 0, a(n) = ceiling((d + n/10^d)^8) where d = 1 + floor(log_10(n)). - Jon E. Schoenfield, Dec 09 2017
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EXAMPLE
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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.
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)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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