A292885 a(n) is the least number k such that k | concat(k-n,k-n+1,…,k,…,k+n-1,k+n).

1, 3, 3, 9, 6, 9, 9, 9, 9, 27, 15, 33, 18, 27, 18, 21, 18, 27, 27, 27, 24, 27, 27, 27, 27, 27, 27, 143, 34, 143, 45, 63, 36, 39, 39, 45, 42, 143, 89, 57, 45, 43, 143, 99, 54, 135, 154, 63, 63, 63, 75, 63, 154, 189, 66, 165, 72, 171, 153, 189, 90, 63, 81, 69, 69

Offset

0,2

Links

Paolo P. Lava, Table of n, a(n) for n = 0..500

Example

a(4) = 6 because concat(2, 3, 4, 5, 6, 7, 8, 9, 10) = 2345678910 is a multiple of 6 and 6 is the least number to have this property.

Maple

P:=proc(q) local a, j, k, n; for k from 1 by 2 to q do for n from 1 to q do a:=n;
for j from 1 to k-1 do a:=a*10^(ilog10(n+j)+1)+n+j; od;
if type(a/(n+(k-1)/2), integer) then print(n+(k-1)/2); break; fi; od; od; end: P(10^9);

Mathematica

Table[SelectFirst[Range[10^3], Function[k, If[And[FreeQ[#, _?(# < 0 &)], First@ # != 0], Divisible[FromDigits@ Flatten@ Map[IntegerDigits, #], k]] &[k + Range[-n, n]] ] ], {n, 0, 64}] (* Michael De Vlieger, Sep 27 2017 *)

Prog

(PARI) isok(k, n) = {my(s = ""); for (i=0, 2*n, s = concat(s, k-n+i); ); (eval(s) % k) == 0; }
a(n) = {my(k = n+1); while(!isok(k, n), k++); k; } \\ Michel Marcus, Oct 06 2017

Crossrefs

Cf. A069860, A069862, A069871, A088797, A088798, A088877.

Sequence in context: A124871 A197414 A247571 * A227075 A165351 A215665

Adjacent sequences: A292882 A292883 A292884 * A292886 A292887 A292888

Keyword

nonn,base,easy

Author

Paolo P. Lava, Sep 26 2017

Status

approved