A232184 Let x(0)x(1)x(2)... x(q) denote the decimal expansion of n. Sequence lists the numbers n > 10 such that x(0)/x(1)x(2)... x(q) + x(0)x(1)/x(2)x(3)... x(q) + ... + x(0)x(1)... x(q-1)/x(q) is an integer.

11, 21, 22, 31, 33, 41, 42, 44, 51, 55, 61, 62, 63, 66, 71, 77, 81, 82, 84, 88, 91, 93, 99, 101, 201, 202, 301, 303, 401, 402, 404, 501, 505, 601, 602, 603, 606, 612, 701, 707, 801, 802, 804, 808, 816, 901, 903, 909, 945, 1001, 1003, 1011, 2001, 2002, 2003

Offset

1,1

Comments

a(n) = A084906(n) for n = 1..24.

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, 11, 22, 11, 33, 11, 44, 22,...

Links

Table of n, a(n) for n=1..55.

Example

945 is in the sequence because 9/45  + 94/5 = 19 is integer.

Maple

with(numtheory):U:=array(1..10):V:=array(1..10):for n from 11 to 3000 do: x:=convert(n, base, 10):n1:=nops(x):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:od:

Crossrefs

Cf. A084906.

Sequence in context: A084854 A108237 A084906 * A232185 A118853 A117841

Adjacent sequences: A232181 A232182 A232183 * A232185 A232186 A232187

Keyword

nonn,base

Author

Michel Lagneau, Nov 20 2013

Status

approved