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Search: id:A124053
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| A124053 |
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Numbers n that can be expressed as the sum of the digits of both m^k and k^m for distinct numbers m and k which are not both equal to powers of 10. |
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+0
2
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| 7, 18, 45, 61, 72, 85, 90, 145, 270, 306, 315, 367, 376, 448, 477, 540, 547, 585, 667, 733, 756, 765, 943, 1152, 1377, 1899, 1971, 2106, 2133, 2155, 2215, 2224, 2349, 2628, 2822, 2871, 2968, 3123, 3139, 3181, 3204, 3355, 3546, 3553, 3775, 3780, 4455, 4582
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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If "sumdigit" denotes the sum of the digits of a number then these are the numbers n such that n=sumdigit(m^k)=sumdigit(k^m).
Two banal cases are not considered: 1) m=k because m^k=k^m and the sum of the digits is authomatically equal for both the numbers; 2) powers of 10 because sumdigit(10^a)=1 for any integer a. The same number can be generated by different pairs: 477 cames from sumdigit(54^63)=sumdigit(63^54) and sumdigit(90^120)=sumdigit(120^90) 2349 cames from sumdigit(216^222)=sumdigit(222^216), sumdigit(216^225)=sumdigit(225^216) and sumdigit(219^222)=sumdigit(222^219)
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EXAMPLE
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270=sumdigit(36^39)=sumdigit(39^36)
1152=sumdigit(114^126)=sumdigit(126^114)
2133=sumdigit(204^213)=sumdigit(213^204)
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MAPLE
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P:=proc(n)local i, j, k, w, x, y; for i from 1 by 1 to n do for j from 1 by 1 to n do w:=0; x:=0; k:=i^j; y:=j^i; while k>0 do w:=w+k-trunc(k/10)*10; k:=trunc(k/10); od; while y>0 do x:=x+y-trunc(y/10)*10; y:=trunc(y/10); od; if (w=x) and (w<>1) and (i<j) then print(i, j, w); fi; od; od; end: P(500);
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CROSSREFS
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Cf. A124359, A124360, A046019, A124365, A124366, A124367.
Sequence in context: A133673 A023166 A002764 this_sequence A084819 A019534 A024830
Adjacent sequences: A124050 A124051 A124052 this_sequence A124054 A124055 A124056
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KEYWORD
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nonn,base
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AUTHOR
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Paolo P. Lava & Giorgio Balzarotti (ppl(AT)spl.at), Nov 03 2006, Nov 29 2006
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