A193415 -id:A193415 - cp's OEIS frontend

A193413 Valley numbers.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 111, 202, 212, 222, 303, 313, 323, 333, 404, 414, 424, 434, 444, 505, 515, 525, 535, 545, 555, 606, 616, 626, 636, 646, 656, 666, 707, 717, 727, 737, 747, 757, 767, 777, 808, 818, 828, 838, 848, 858, 868, 878, 888, 909, 919, 929, 939, 949, 959, 969, 979, 989, 999, 1001

Offset: 1

Jaroslav Krizek, Jul 25 2011

For n > 10 the structure of digits represents a valley. The first digit is equal to the last digit (1 - 9). The first digits are in nonincreasing order. The last digits are in nondecreasing order. The numbers may have more than one smallest digit. Sequence is infinite.
Superset of crater numbers (A193409) and A193412.
See valley numbers in base 2 (A193414 and A193415).

			Illustration using 6543333346:
  6 . . . . . . . . 6
  . 5 . . . . . . . .
  . . 4 . . . . . 4 .
  . . . 3 3 3 3 3 . .

Cf. A110785, A193409, A193412, A193414, A193415.

Cf. A134970. - Omar E. Pol, Aug 05 2011

More terms extended by definition by Jaroslav Krizek, Jul 27 2011

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

Original entry on oeis.org

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

Jaroslav Krizek, Jul 25 2011

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, ...}.

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

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

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

First term corrected by Jaroslav Krizek, Jul 27 2011

cp's OEIS Frontend

A193413 Valley numbers.

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