A248954 - OEIS

%I #20 Oct 23 2014 21:04:39

%S 1,2,3,4,5,6,7,8,9,11,22,33,44,55,66,77,88,99,111,142,214,222,284,333,

%T 421,428,444,555,666,777,842,888,999,1111,1142,1212,1242,1346,1421,

%U 1422,1442,2114,2121,2124,2142,2144,2214,2222,2284,2421,2424,2484,2842,2844

%N 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.

%C Similar to A227001.

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

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

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

%H Paolo P. Lava, <a href="/A248954/b248954.txt">Table of n, a(n) for n = 1..1000</a>

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

%p with(numtheory):P:=proc(q) local a,b,c,k,n,ok; for n from 1 to q do ok:=1; a:=n;

%p for k from 1 to ilog10(n)+1 do if (a mod 10)=0 then ok:=0; break; else a:=trunc(a/10);

%p fi; od; if ok=1 then a:=0; b:=n;

%p for k from 1 to ilog10(n) do c:=b mod 10;  b:=trunc(b/10); a:=a+c/(b mod 10); od;

%p if type(a+trunc(n/10^ilog10(n))/(n mod 10),integer) then print(n); fi; fi; od; end: P(10^6);

%Y CF. A227001.

%K nonn,base,easy

%O 1,2

%A _Paolo P. Lava_, Oct 21 2014