A193414 Numbers m such that written in base 2 the structure of digits represents a valley.

1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 23, 25, 27, 29, 31, 33, 35, 39, 47, 49, 51, 55, 57, 59, 61, 63, 65, 67, 71, 79, 95, 97, 99, 103, 111, 113, 115, 119, 121, 123, 125, 127, 129, 131, 135, 143, 159, 191, 193, 195, 199, 207, 223, 225, 227, 231, 239, 241, 243

Offset: 1

Author

Jaroslav Krizek, Jul 25 2011

Keywords

• nonn
• base

Comments

For n > 1 the structure of digits of numbers written in base 2 represents a valley. The first digit is equal to the last digit (1). The first digits are in nonincreasing order. The last digits are in nondecreasing order. The numbers may have more than one 0 digit. Sequence is infinite.

See A193415: numbers m written in base 2: {1, 11, 101, 111, 1001, 1011, 1101, 1111, ...}.

Examples

			Illustration using 67 = 1000011_2:
  1  .  .  .  .  1  1
  .  0  0  0  0  .  .
		

Crossrefs

Cf. A193413 (Valley numbers written in base 10), A193415.

Programs

Mathematica

Select[Range[300], MemberQ[{1, 3}, Length[Split[IntegerDigits[#, 2]]]] &] (* T. D. Noe, Jul 26 2011 *)

Extensions

First term corrected by Jaroslav Krizek, Jul 27 2011