OFFSET
1,2
COMMENTS
By "run" of 0's or 1's, it is meant: Think of binary k as a string of 0's and 1's. A single run of the digit b (0 or 1) is made up completely of consecutive digits all equal to b, and is bounded on its ends by either the digit 1-b or the end of the string.
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..400
EXAMPLE
For n = 9, we check: 9 in binary is 1001, which has a run of two 0's, and 2 does not divide 9. Checking further: 2*9 = 18 = 10010, which still doesn't work. 3*9 = 27 = 11011 in binary, which has two runs of two 1's. 4*9 = 36 = 100100 in binary, 5*9 = 45 = 101101 in binary, 6*9 = 54 = 110110 in binary, 7*9 = 63 = 111111 in binary, 8*9 = 72 = 1001000 in binary, none of which work. But 9*9 = 81 = 1010001 in binary, which has three runs of one 1 each, a run of one 0, and a run of three 0's. Since 9 is divisible by both of these lengths (1 and 3), a(9) = 81.
MATHEMATICA
a[n_] := Block[{m}, If[n>2 && PrimeQ[n], m=1; While[Mod[m, n] > 0, m=4*m+1], m=n; While[! AllTrue[ Union[ Length /@ Split[ IntegerDigits[m, 2]]], Mod[n, #] == 0 &], m += n]]; m]; Array[a, 60] (* Giovanni Resta, Aug 11 2019 *)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Leroy Quet, Jul 05 2009
EXTENSIONS
More terms from Sean A. Irvine, Jan 26 2011
More terms from Giovanni Resta, Aug 11 2019
STATUS
approved