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A282766 n/2 analog of Keith numbers. 4
50, 642, 1284, 1926, 2292, 5088, 29828, 42922, 53046, 95968, 512050, 1043160, 1723714, 14819056, 154860206, 159251186, 752516578, 946218018, 54728972948 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Like Keith numbers but starting from n/2 digits to reach n.

Consider the digits of n/2. 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.

If it exists, a(20) > 10^12. - Lars Blomberg Mar 13 2017

LINKS

Table of n, a(n) for n=1..19.

EXAMPLE

642/2 = 321:

3 + 2 + 1 = 6;

2 + 1 + 6 = 9;

1 + 6 + 9 = 16;

6 + 9 + 16 = 31;

9 + 16 + 31 = 56;

16 + 31 + 56 = 103;

31 + 56 + 103 = 190;

56 + 103 + 190 = 349;

103 + 190 + 349 = 642.

MAPLE

with(numtheory): P:=proc(q, h, w) local a, b, k, n, t, v; v:=array(1..h);

for n from 1/w by 1/w 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, 1/2);

MATHEMATICA

With[{n = 2}, Select[Range[10 n, 10^6, n], Function[k, Last@ NestWhile[Append[Rest@ #, Total@ #] &, IntegerDigits[k/n], Total@ # <= k &] == k]]] (* Michael De Vlieger, Feb 27 2017 *)

CROSSREFS

Cf. A282757-A282765, A282767, A282768, A282769.

Sequence in context: A231583 A156965 A240385 * A323485 A052460 A224168

Adjacent sequences:  A282763 A282764 A282765 * A282767 A282768 A282769

KEYWORD

nonn,base,more

AUTHOR

Paolo P. Lava, Feb 27 2017

EXTENSIONS

a(15)-a(19) from Lars Blomberg, Mar 13 2017

STATUS

approved

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Last modified February 17 15:32 EST 2020. Contains 331998 sequences. (Running on oeis4.)