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A282758
3*n analog to Keith numbers.
2
7, 9, 14, 19, 21, 28, 38, 53, 54, 76, 92, 124, 1299, 18185, 20468, 31871, 32054, 37903, 128200, 152057, 175539, 193399, 214631, 303677, 1806425, 3250457, 3616693, 7870170, 10793441, 12047403, 13781464, 15035426, 18663611, 19917573, 22905596, 46531972, 101743590
OFFSET
1,1
COMMENTS
Like Keith numbers but starting from 3*n digits to reach n.
Consider the digits of 3*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
3*28 = 84:
8 + 4 = 12;
4 + 12 = 16;
12 + 16 = 28.
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, 3);
MATHEMATICA
Select[Range[10^6], Function[n, Module[{d = IntegerDigits[3 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 *)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Paolo P. Lava, Feb 22 2017
STATUS
approved