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Search: id:A135740
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| A135740 |
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Maximal sum of decimal digits of a^b for 1 <= a,b <= n. |
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+0
1
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| 1, 4, 9, 13, 13, 27, 36, 37, 45, 45, 62, 64, 71, 97, 99, 99, 109, 117, 127, 136, 136, 148, 153, 163, 171, 197, 197, 202, 224, 224, 236, 236, 251, 256, 281, 281, 302, 302, 306, 306, 315, 352, 352, 355, 360, 385, 385, 396, 406, 406, 431, 432, 437, 441, 469, 469
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Clearly a(n) <= a(n+1). For what values of n do we have equality? Is there an explicit formula for a(n)?
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LINKS
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Project Euler, Problem 56: Considering natural numbers of the form a^b, find the maximum digital sum.
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EXAMPLE
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a(3)=9=2+7 is the digit sum of 3^2 and 3^3=27, all other a^b with a,b <= 3 have smaller digit sum.
a(4)=13=2+5+6 is the digit sum of 4^4=256, all other a^b with a,b <= 4 have smaller digit sum.
a(5)=13 since also for a,b <= 5 there is no higher digit sum (but the same is obtained for 5^4=625).
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MATHEMATICA
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a = {1}; For[n = 2, n < 100, n++, r = a[[ -1]]; For[j = 1, j < n + 1, j++, If[Max[Plus @@ IntegerDigits[n^j], Plus @@ IntegerDigits[j^n]] > r, r = Max[Plus @@ IntegerDigits[n^j], Plus @@ IntegerDigits[j^n]]]]; AppendTo[a, r]]; a - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Dec 22 2007
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PROGRAM
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(PARI) digitsum(n, s)=n=[n]; while(n, n=divrem(n[1], 10); s+=n[2]); s A135740(n)=vecmax(matrix(n, n, i, j, digitsum(i^j)))
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CROSSREFS
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Adjacent sequences: A135737 A135738 A135739 this_sequence A135741 A135742 A135743
Sequence in context: A055381 A032820 A066588 this_sequence A010412 A033662 A136640
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KEYWORD
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base,nonn
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AUTHOR
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M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Nov 30 2007
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EXTENSIONS
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More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Dec 22 2007
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