A265730 Zeroless numbers n such that the decimal expansion of a/b contains each digit of n, for all a,b > 0 such that concatenate(a,b) = n.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 16, 17, 27, 47, 52, 57, 78, 87, 117, 131, 151, 157, 158, 161, 171, 177, 187, 191, 247, 257, 277, 417, 447, 457, 487, 517, 547, 557, 558, 587, 592, 717, 747, 757, 787, 817, 857, 887, 1131, 1147, 1151, 1157, 1161, 1167, 1171, 1177, 1181, 1191, 1221, 1247, 1251, 1257, 1261, 1287, 1331, 1361, 1371, 1417

Offset

1,2

Comments

Termed "1951 numbers" by Eric Angelini, cf. LINKS.

Links

Table of n, a(n) for n=1..68.

E. Angelini, 1951-numbers, SeqFan list, Dec 14, 2015.

Example

The single-digit numbers 1,...,9 are in the sequence because there is no possible decomposition a,b.
The number 1951 is in the sequence because 195/1 = 195.0, 19/51 = 0.3725490196... and 1/951 = 0.0010515247108307045215562565720294... all have each of the digits '1', '5' and '9' the number 1951 is made of.

Mathematica

fQ[n_] := Block[{d = IntegerDigits@ n, w}, w = Map[Union@ Flatten@ # &, First /@ RealDigits@ Map[FromDigits@ Take[d, #]/FromDigits@ Take[d, -Length@ d + #] &, Reverse@ Range[Length@ d - 1]], {1}]; And @@ Function[k, AllTrue[d, MemberQ[k, #] &]] /@ w]; Select[Select[Range@ 1500, Last@ DigitCount@ # == 0 &], fQ] (* Michael De Vlieger, Dec 14 2015 *)

Prog

(PARI) is(n, d=Set(digits(n)), p=n+#Str(n))={vecmin(d)&&!for(i=10, n, setminus(d, Set(digits(n\i*10^p\(n%i))))&&return; i=i*10-1)}

Crossrefs

Cf. A051626.

Sequence in context: A190296 A143288 A001103 * A304248 A147591 A271954

Adjacent sequences: A265727 A265728 A265729 * A265731 A265732 A265733

Keyword

nonn,base

Author

Eric Angelini and M. F. Hasler, Dec 14 2015

Status

approved