login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A282767 n/3 analog of Keith numbers. 2
45, 609, 1218, 1827, 3213, 21309, 28206, 29319, 31917, 39333, 47337, 78666, 102090, 117999, 204180, 406437, 302867592, 4507146801, 5440407522 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Like Keith numbers but starting from n/3 digits to reach n.

Consider the digits of n/3. 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

609/3 = 203:

2 + 0 + 3 = 5;

0 + 3 + 5 = 8;

3 + 5 + 8 = 16;

5 + 8 + 16 = 29;

8 + 16 + 29 = 53;

16 + 29 + 53 = 98;

29 + 53 + 98 = 180;

53 + 98 + 180 = 331;

98 + 180 + 331 = 609.

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, 1/3);

MATHEMATICA

With[{n = 3}, 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, A282768, A282769.

Sequence in context: A160838 A189350 A090024 * A160234 A110691 A296540

Adjacent sequences: A282764 A282765 A282766 * A282768 A282769 A282770

KEYWORD

nonn,base,more

AUTHOR

Paolo P. Lava, Feb 27 2017

EXTENSIONS

a(17)-a(19) from Lars Blomberg, Mar 13 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 6 11:50 EST 2022. Contains 358632 sequences. (Running on oeis4.)