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A281916
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5th power analog of Keith numbers.
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9
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1, 28, 35, 36, 46, 51, 99, 109, 191, 239, 476, 491, 1022, 1126, 1358, 1362, 15156, 21581, 44270, 63377, 100164, 375830, 388148, 2749998, 5215505, 10158487, 81082532, 87643314, 410989134, 1485204944, 3496111364, 3829840893, 15889549579, 16107462404, 16766005098, 17608009898
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OFFSET
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1,2
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COMMENTS
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Like Keith numbers but starting from n^5 digits to reach n.
Consider the digits of n^5. Take their sum and repeat the process deleting the first addend and adding the previous sum. The sequence lists the numbers that after some number of iterations reach a sum equal to n.
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LINKS
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EXAMPLE
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109^5 = 15386239549:
1 + 5 + 3 + 8 + 6 + 2 + 3 + 9 + 5 + 4 + 9 = 55;
5 + 3 + 8 + 6 + 2 + 3 + 9 + 5 + 4 + 9 + 55 = 109.
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MAPLE
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with(numtheory): P:=proc(q, h, w) local a, b, k, t, v; global n; v:=array(1..h);
for n from 1 to q do b:=n^w; a:=[];
for k from 1 to ilog10(b)+1 do a:=[(b mod 10), op(a)]; b:=trunc(b/10); od;
for k from 1 to nops(a) do v[k]:=a[k]; od; b:=ilog10(n^w)+1;
t:=nops(a)+1; v[t]:=add(v[k], k=1..b); while v[t]<n do t:=t+1; v[t]:=add(v[k], k=t-b..t-1);
od; if v[t]=n then print(n); fi; od; end: P(10^6, 10000, 5);
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MATHEMATICA
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(* function keithQ[ ] is defined in A007629 *)
a281916[n_] := Join[{1}, Select[Range[10, n], keithQ[#, 5]&]]
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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