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Search: id:A130179
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| A130179 |
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Largest k such that k <= 81*(number of digits of k^n)*(number of digits of k^(n+1)). |
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+0
5
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| 2268, 7776, 18954, 35397, 56376, 85050, 119556, 159894, 209952, 267300, 331047, 402084, 479520, 570807, 670032, 777195, 892296, 1015335, 1146312, 1285227, 1432080, 1586871, 1749600, 1932498, 2125035, 2312712, 2522340, 2741607
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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a(n) is an upper bound for A130181(n) and all the more so for A126783(n); apparently even A130181(n) < a(n)/4.
All terms are divisible by 81; the quotients a(n)/81 are in A130085.
For some n (18, 34, 35, 38, 42, 58, 59, ...) the line y = x and the graph of the staircase function y = 81*(number of digits of x^n)*(number of digits of x^(n+1)) intersect twice; this possibility has to be taken into account by the program.
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LINKS
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Klaus Brockhaus, Table of n, a(n) for n=1..100
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EXAMPLE
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Let D(n,k) = 81*(number of digits of k^n)*(number of digits of k^(n+1)).
D(2,k) > k for k = 1..4641, D(2,k) = 7776 for k = 4642..9999, D(2,k) < k for k >= 10000, hence a(2) = 7776.
D(18,k) > k for k = 1..885866, D(18,k) = 997272 for k = 885867..999999, D(18,k) = 1015335 for k = 1000000..1128837, D(18,k) < k for k >= 1128838, hence a(18) = 1015335.
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PROGRAM
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(PARI) {for(n=1, 28, s=30*n; k=s; while(k<81*length(Str(k^n))*length(Str(k^(n+1))), k+=s); r=0; g=0; k-=s; b=1; while(b, p=81*length(Str(k^n))*length(Str(k^(n+1))); if(r<p, r=p; h=r; if(k>r, b=0, g=h)); k++); print1(g, ", "))}
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CROSSREFS
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Cf. A126783, A130181, A130085.
Sequence in context: A035873 A046168 A154673 this_sequence A125253 A059466 A166222
Adjacent sequences: A130176 A130177 A130178 this_sequence A130180 A130181 A130182
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KEYWORD
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nonn,base
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AUTHOR
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Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), May 20 2007
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