A282762 -id:A282762 - cp's OEIS frontend

A282761 6*n analog to Keith numbers.

9, 23, 85, 88, 208, 953, 12339, 122420, 251925, 286400, 467608, 1207360, 1308519, 1537214, 1638373, 1844108, 2314739, 2736742, 9331102, 11692851, 28349534, 85403569

Offset: 1

Paolo P. Lava, Feb 22 2017

Like Keith numbers but starting from 6*n digits to reach n.

Consider the digits of 6*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.

			6*23 = 138:
1 + 3 + 8 = 12;
3 + 8 + 12 = 23.

Cf. A282757 - A282760, A282762 - A282765.

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]

Select[Range[10^6], Function[n, Module[{d = IntegerDigits[6 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 *)

A282763 8*n analog to Keith numbers.

Original entry on oeis.org

9, 20, 176, 184, 277, 2669, 15705, 233202, 241202, 445657, 742714, 2095479, 4697536, 10508788, 20308656, 55683878, 86603874

Offset: 1

Paolo P. Lava, Feb 22 2017

Like Keith numbers but starting from 8*n digits to reach n.

Consider the digits of 8*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.

			8*20 = 160:
1 + 6 + 0 = 7;
6 + 0 + 7 = 13;
0 + 7 + 13 = 20.

Cf. A282757 - A282762, A282764, A282765.

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]

Select[Range[10^6], Function[n, Module[{d = IntegerDigits[8 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 *)

cp's OEIS Frontend

A282761 6*n analog to Keith numbers.

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