OFFSET
1,1
COMMENTS
Subsequence of A232184. This sequence is probably finite (no further terms less than 2*10^8).
The corresponding integers are 1, 2, 1, 3, 1, 4, 2, 1, 5, 1, 6, 3, 2, 1, 7, 1, 8, 4, 2, 1, 9, 3, 1, 31, 14, 19.
EXAMPLE
945 is in the sequence because 9/45 + 94/5 = 19 is an integer.
MAPLE
with(numtheory):U:=array(1..10):V:=array(1..10):for n from 1 to 20000 do: x:=convert(n, base, 10):n1:=nops(x): s:=product('x[i]', 'i'=1..n1):if s<>0 then s1:=0:s2:=0:for i from 1 to n1 do:s1:=s1+x[i]*10^(i-1): U[i]:=s1:od: s2:=x[n1]:V[n1]:=s2:for j from n1-1 by -1 to 1 do:s2:=s2*10+x[j]:V[j]:=s2:od:s3:=0:ii:=0:for k from n1 by -1 to 2 while(ii=0) do:if U[k-1]=0 then ii:=1: else s3:=s3+V[k]/U[k-1]:fi:od:if s3=floor(s3) and ii=0 then printf(`%d, `, n):else fi:fi:od:
PROG
(PARI) isok(k) = my(d=digits(k)); if (vecmin(d), denominator(sum(j=1, #d-1, fromdigits(Vec(d, j))/fromdigits(vector(#d, k, if (k>j, d[k])))))==1); \\ Michel Marcus, Jan 11 2025
CROSSREFS
KEYWORD
nonn,base,more
AUTHOR
Michel Lagneau, Nov 20 2013
STATUS
approved
