1,2

By "run" of 0's or 1's, it is meant: Think of binary n 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 by the edge of the string.

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), then a(9) = 81.

A162534, A162537

Sequence in context: A055746 A060600 A143247 this_sequence A100980 A122509 A024230

Adjacent sequences: A162533 A162534 A162535 this_sequence A162537 A162538 A162539

base,more,nonn

Leroy Quet (q1qq2qqq3qqqq(AT)yahoo.com), Jul 05 2009