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A282765
10*n analog to Keith numbers.
13
1, 2, 3, 4, 5, 6, 7, 8, 9, 14, 19, 28, 56, 176, 904, 3347, 4795, 5301, 9775, 10028, 16165, 16715, 35103, 49693, 111039, 191103, 370287, 439385, 845772, 1727706, 1836482, 3631676, 3767812, 4363796, 4499932, 5351605, 6940437, 20090073, 28246243, 38221997, 60220332
OFFSET
1,2
COMMENTS
Like Keith numbers but starting from 10*n digits to reach n.
Consider the digits of 10*n. Take their sum and repeat the process deleting the first addend and adding the previous sum. The sequence lists the numbers that after some iterations reach a sum equal to themselves.
EXAMPLE
10*14 = 140:
1 + 4 + 0 = 5;
4 + 0 + 5 = 9;
0 + 5 + 9 = 14.
MAPLE
with(numtheory): P:=proc(q, h, w) local a, b, k, n, t, v; v:=array(1..h);
for n from 1 to q do a:=w*n; b:=ilog10(a)+1; if b>1 then
for k from 1 to b do v[b-k+1]:=(a mod 10); a:=trunc(a/10); od; t:=b+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; fi; od; end: P(10^6, 1000, 10);
MATHEMATICA
Select[Range[10^6], Function[n, Module[{d = IntegerDigits[10 n], s, k = 0}, s = Total@ d; While[s < n, AppendTo[d, s]; k++; s = 2 s - d[[k]]]; s == n]]] (* Michael De Vlieger, Feb 22 2017, after T. D. Noe at A007629 *)
CROSSREFS
Sequence in context: A085153 A339111 A130010 * A033081 A032579 A151543
KEYWORD
nonn,base
AUTHOR
Paolo P. Lava, Feb 22 2017
STATUS
approved