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A282769 n/7 analog of Keith numbers. 4
301, 602, 1113, 4942, 478205, 23942940, 47885880, 178114489749 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Like Keith numbers but starting from n/7 digits to reach n.
Consider the digits of n/7. 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(9) > 10^12. - Lars Blomberg Mar 07 2017
LINKS
EXAMPLE
1113/7 = 159:
1 + 5 + 9 = 15;
5 + 9 + 15 = 29;
9 + 15 + 29 = 53;
15 + 29 + 53 = 97;
29 + 53 + 97 = 179;
53 + 97 + 179 = 329;
97 + 179 + 329 = 605;
179 + 329 + 605 = 1113.
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, 1/7);
MATHEMATICA
With[{n = 7}, 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
Sequence in context: A004226 A297913 A298506 * A256101 A070192 A298326
KEYWORD
nonn,base,more
AUTHOR
Paolo P. Lava, Feb 27 2017
EXTENSIONS
a(8) from Lars Blomberg, Mar 07 2017
STATUS
approved

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Last modified April 20 22:14 EDT 2024. Contains 371848 sequences. (Running on oeis4.)