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Search: id:A126783
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| A126783 |
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Smallest k > 1 such that (sum of digits of k^n)*(sum of digits of k^(n+1)) = k, or 0 if no such k exists. |
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+0
4
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| 80, 80, 70, 3905, 4004, 700, 19278, 32761, 5600, 8100, 24940, 10600, 56330, 68040, 81760, 149705, 116180, 126360, 123580, 0, 65500, 311003, 205030, 114400, 454951, 317350, 312170, 296270, 359380, 332750, 699785, 723338, 498150, 499130, 901368
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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For each n there is an upper bound (see A130179) for values of k such that (sum of digits of k^n)*(sum of digits of k^(n+1)) = k, hence the number of such k is finite, possibly zero, (see A130180) and if the number is not zero there is a largest one (see A130181).
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LINKS
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Klaus Brockhaus, Table of n, a(n) for n=1..54
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EXAMPLE
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For n = 2 the smallest such k is 80: 80^2 = 6400 and 6+4+0+0 = 10; 80^3 = 512000 and 5+1+2+0+0+0 = 8; 10*8 = 80. Hence a(2) = 80.
For n = 3 the smallest such k is 70: 70^3 = 343000 and 3+4+3+0+0+0 = 10; 70^4 = 24010000 and 2+4+0+1+0+0+0+0 = 7; 10*7 = 70. Hence a(3) = 70.
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MAPLE
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P:=proc(n) local a, i, j, k, w, x; for a from 1 by 1 to n do for i from 1 by 1 to n*n do w:=0; k:=i^a; j:=0; x:=i^(a+1); while k>0 do w:=w+k-(trunc(k/10)*10); k:=trunc(k/10); od; while x>0 do j:=j+x-(trunc(x/10)*10); x:=trunc(x/10); od; if (i=w*j and i>1) then print(i); break; fi; od; od; end: P(1000);
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CROSSREFS
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Cf. A130179, A130180, A130181.
Sequence in context: A050456 A107930 A033400 this_sequence A114836 A069086 A119482
Adjacent sequences: A126780 A126781 A126782 this_sequence A126784 A126785 A126786
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KEYWORD
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hard,nonn,base
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AUTHOR
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Paolo P. Lava & Giorgio Balzarotti (ppl(AT)spl.at), Apr 17 2007
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EXTENSIONS
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Edited and a(17) to a(35) added by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), May 14 2007
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