A282763 -id:A282763 - cp's OEIS frontend

A282762 7*n analog to Keith numbers.

3, 6, 9, 12, 25, 29, 33, 58, 62, 66, 70, 87, 91, 95, 99, 124, 128, 150, 152, 165, 178, 191, 204, 217, 592, 801, 1184, 3860, 15728, 59800, 117711, 157701, 230720, 270737, 496085, 795918, 869366, 954639, 1549319, 1826773, 3169440, 3170466, 3973793, 3974819, 3975845, 4012718, 4013744, 5120160, 5653357, 5978943

Offset: 1

Paolo P. Lava, Feb 22 2017

Like Keith numbers but starting from 7*n digits to reach n.

Consider the digits of 7*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.

			7*25 = 175:
1 + 7 + 5 = 13;
7 + 5 + 13 =25.

Cf. A282757 - A282761, A282763 - 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[7 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 *)

A282764 9*n analog to Keith numbers.

Original entry on oeis.org

9, 17, 48, 55, 96, 120, 124, 131, 244, 426, 787, 1893, 5307, 5364, 5600, 10083, 31085, 46733, 52700, 53456, 56857, 56920, 109620, 110313, 110376, 374016, 2989245, 4081505, 5173765, 13017112, 17242512, 34346372, 34638676

Offset: 1

Paolo P. Lava, Feb 22 2017

Like Keith numbers but starting from 9*n digits to reach n.

Consider the digits of 9*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.

			9*17 = 153:
1 + 5 + 3 = 9;
5 + 3 + 9 = 17.

Cf. A282757 - A282763, 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[9 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

A282762 7*n analog to Keith numbers.

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