login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A282768 n/5 analog of Keith numbers. 3
55, 110, 165, 220, 275, 330, 385, 440, 495, 530, 47270, 119710, 685385, 21526000, 6055017240 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Like Keith numbers but starting from n/5 digits to reach n.

Consider the digits of n/5. 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(16) > 10^12. - Lars Blomberg Mar 07 2017

LINKS

Table of n, a(n) for n=1..15.

EXAMPLE

530/5 = 106:

   1 +   0 +   6 =   7;

   0 +   6 +   7 =  13;

   6 +   7 +  13 =  26;

   7 +  13 +  26 =  46;

  13 +  26 +  46 =  85;

  26 +  46 +  85 = 157;

  46 +  85 + 157 = 288;

  85 + 157 + 288 = 530.

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, 1/5);

MATHEMATICA

With[{n = 5}, 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, A282766, A282767, A282769.

Sequence in context: A118151 A277273 A275124 * A217429 A154031 A044242

Adjacent sequences:  A282765 A282766 A282767 * A282769 A282770 A282771

KEYWORD

nonn,base,more

AUTHOR

Paolo P. Lava, Feb 27 2017

EXTENSIONS

a(15) from Lars Blomberg, Mar 07 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 22 04:06 EDT 2021. Contains 345367 sequences. (Running on oeis4.)