A077306 Smallest multiple of n formed by the concatenation of n successive numbers, or 0 if no such number exists.

1, 12, 123, 3456, 12345, 123456, 3456789, 56789101112, 123456789, 12345678910, 910111213141516171819, 123456789101112, 45678910111213141516, 7891011121314151617181920, 123456789101112131415, 567891011121314151617181920

Offset: 1

Author

Amarnath Murthy, Nov 03 2002

Keywords

• base
• nonn

Links

• Paul Tek, Table of n, a(n) for n = 1..333

Crossrefs

Cf. A075000, A077308.

Programs

Maple

digs := proc(inp::integer) local resul,shiftinp : resul := 1 : shiftinp := iquo(inp,10) : while shiftinp > 0 do resul := resul+1 : shiftinp := iquo(shiftinp,10) : od : RETURN(resul) : end: # provide number of concatenation of frst up to lst newnum := proc(frst::integer,lst::integer) local resul,i : resul:= frst : for i from frst+1 to lst do resul := resul*10^digs(i)+i : od : RETURN(resul) ; end : n := 1 : while n < 20 do nold := n : newfeedstrt := 1 : newfeedend := newfeedstrt + n-1 : while nold = n do trythis := newnum(newfeedstrt,newfeedend) : if ( trythis mod n ) = 0 then printf("%a,",trythis) ; n := n+ 1: break : fi : newfeedstrt := newfeedstrt + 1 : newfeedend := newfeedstrt + n-1 : od : od : # R. J. Mathar, Mar 13 2006

Mathematica

a[n_] := Block[{v, k = 1}, While[Mod[v = FromDigits@ Flatten@ IntegerDigits@ Range[k, k+n-1], n] > 0, k++]; v]; Array[a,20] (* Giovanni Resta, May 12 2013 *)

Extensions

More terms from R. J. Mathar, Mar 13 2006