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!)
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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 10 05:05 EDT 2021. Contains 343748 sequences. (Running on oeis4.)