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
Examples
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.
Links
- Paolo P. Lava, Table of n, a(n) for n = 0..500
Programs
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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);
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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 *)
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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