Search: id:A125526
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%I A125526
%S A125526 1,22,34,43,54,81,82,169,187
%N A125526 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)).
%C A125526 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
%e A125526 a(2)=22 because 2+2=4, 22^4=234256, 2+3+4+2+5+6=22.
%p A125526 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);
%p A125526 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
%p A125526 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
%Y A125526 Cf. A124053, A124359, A124360, A046019, A124365, A124366, A124367.
%Y A125526 Sequence in context: A020151 A071265 A103320 this_sequence A124317 A159518 
               A100039
%Y A125526 Adjacent sequences: A125523 A125524 A125525 this_sequence A125527 A125528 
               A125529
%K A125526 easy,fini,nonn,full,base
%O A125526 0,2
%A A125526 Paolo P. Lava & Giorgio Balzarotti (ppl(AT)spl.at), Jan 22 2007

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