A248954 Let x0 x1 x2...xq denote the decimal expansion of n. Sequence lists numbers n such that x1/x0 + x2/x1 +...+ x0/xq is an integer.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 111, 142, 214, 222, 284, 333, 421, 428, 444, 555, 666, 777, 842, 888, 999, 1111, 1142, 1212, 1242, 1346, 1421, 1422, 1442, 2114, 2121, 2124, 2142, 2144, 2214, 2222, 2284, 2421, 2424, 2484, 2842, 2844

Offset

1,2

Comments

Similar to A227001.

The primitive values are 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 111, 142, 1111, 1142,...

284 is not a primitive value because each digit equals two times each digit of 142.

214 is not a primitive value because 214 is a cyclic permutation of 142.

Links

Paolo P. Lava, Table of n, a(n) for n = 1..1000

Example

3461 is in the sequence because 1/6 + 6/4 + 4/3 + 3/1 = 6.

Maple

with(numtheory):P:=proc(q) local a, b, c, k, n, ok; for n from 1 to q do ok:=1; a:=n;
for k from 1 to ilog10(n)+1 do if (a mod 10)=0 then ok:=0; break; else a:=trunc(a/10);
fi; od; if ok=1 then a:=0; b:=n;
for k from 1 to ilog10(n) do c:=b mod 10;  b:=trunc(b/10); a:=a+c/(b mod 10); od;
if type(a+trunc(n/10^ilog10(n))/(n mod 10), integer) then print(n); fi; fi; od; end: P(10^6);

Crossrefs

CF. A227001.

Sequence in context: A346217 A353729 A227001 * A082937 A214019 A160818

Adjacent sequences: A248951 A248952 A248953 * A248955 A248956 A248957

Keyword

nonn,base,easy

Author

Paolo P. Lava, Oct 21 2014

Status

approved