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Search: id:A125526
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| A125526 |
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Numbers n for which the sum of the digits of n raised to the sum of the digits of n itself is equal to n. If "sumdigit" denotes the sum of the digits of a number then these are the numbers n such that n=sumdigit(n^sumdigit(n)). |
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+0
5
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OFFSET
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0,2
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COMMENT
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There are no other terms. Proof: Assume the next terms has d digits. 10^d > n >= 10^(d-1); sumdigit(n) >= 9d; n^sumdigit(n) < (10^d)^(9d) < 10^(9d^2); 9*(9d^2+1) > sumdigit(n^sumdigit(n)); 9*(9d^2+1) > n 9*(9d^2+1) > 10^(d-1). So d<5. - Fung Cheok Yin (cheokyin_restart(AT)yahoo.com.hk), Mar 11 2007
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EXAMPLE
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a(2)=22 because 2+2=4, 22^4=234256, 2+3+4+2+5+6=22.
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MAPLE
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P:=proc(n) local i, j, k, w; for i from 1 by 1 to n do w:=0; k:=i; while k>0 do w:=w+k-trunc(k/10)*10; k:=trunc(k/10); od; k:=i^w; w:=0; while k>0 do w:=w+k-trunc(k/10)*10; k:=trunc(k/10); od; if (i=w) then print(w); fi; od; end: P(200);
sod := proc(n, b) convert(convert(n, base, b), `+`) end; b:=10: L:=[]: for w to 1 do for n from 1 to 10^3 do x:=sod(n^sod(n, b), b); if x=n then print(n); L:=[op(L), n]; fi; od od; L; - Walter A. Kehowski (wkehowski(AT)cox.net), Feb 12 2007
sd:=proc(n) local nn: nn:=convert(n, base, 10): sum(nn[j], j=1..nops(nn)) end: a:=proc(n) if sd(n^sd(n))=n then n else fi end: seq(a(n), n=1..500); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 16 2007
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CROSSREFS
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Cf. A124053, A124359, A124360, A046019, A124365, A124366, A124367.
Adjacent sequences: A125523 A125524 A125525 this_sequence A125527 A125528 A125529
Sequence in context: A020151 A071265 A103320 this_sequence A124317 A100039 A061561
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KEYWORD
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easy,fini,nonn,full,base
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AUTHOR
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Paolo P. Lava & Giorgio Balzarotti (ppl(AT)spl.at), Jan 22 2007
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