A227001 Let x0 x1 x2...xq denote the decimal expansion of n. Sequence lists numbers n such that x0/x1 + x1/x2 + ... + xq/x0 is an integer.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 111, 124, 222, 241, 248, 333, 412, 444, 482, 555, 666, 777, 824, 888, 999, 1111, 1124, 1212, 1224, 1241, 1242, 1244, 1643, 2121, 2124, 2222, 2241, 2248, 2411, 2412, 2421, 2424, 2441, 2448, 2482

Offset

1,2

Comments

The primitive values are 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 111, 124, 1111, 1124, ...

248 is not a primitive value because each digit equals two times each digit of 124.

241 is not a primitive value because 241 is a cyclic permutation of 124.

Links

Michel Lagneau, Table of n, a(n) for n = 1..10000

Example

3164 is in the sequence because 3/1 + 1/6 + 6/4 + 4/3 = 6 is integer.

Maple

for n from 1 to 4000 do: x:=convert(n, base, 10):n1:=nops(x): p:= product('x[i]', 'i'=1..n1):if p<>0 then: s:=sum('x[n1-i+1]/x[n1-i]', 'i'=1..n1-1):s:=s+x[1]/x[n1]: if s=floor(s) then printf(`%d, `, n):else fi:fi:od:

Crossrefs

Sequence in context: A368944 A346217 A353729 * A248954 A082937 A214019

Adjacent sequences: A226998 A226999 A227000 * A227002 A227003 A227004

Keyword

nonn,base

Author

Michel Lagneau, Jun 26 2013

Status

approved