A193414 - OEIS

%I #24 Aug 03 2022 02:33:39

%S 1,3,5,7,9,11,13,15,17,19,23,25,27,29,31,33,35,39,47,49,51,55,57,59,

%T 61,63,65,67,71,79,95,97,99,103,111,113,115,119,121,123,125,127,129,

%U 131,135,143,159,191,193,195,199,207,223,225,227,231,239,241,243

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

%C 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.

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

%e Illustration using 67 = 1000011_2:

%e   1  .  .  .  .  1  1

%e   .  0  0  0  0  .  .

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

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

%K nonn,base

%O 1,2

%A _Jaroslav Krizek_, Jul 25 2011

%E First term corrected by _Jaroslav Krizek_, Jul 27 2011