A193412 -id:A193412 - 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

A193409 Crater numbers.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 101, 212, 323, 434, 545, 656, 767, 878, 989, 21012, 32123, 43234, 54345, 65456, 76567, 87678, 98789, 3210123, 4321234, 5432345, 6543456, 7654567, 8765678, 9876789, 432101234, 543212345, 654323456, 765434567, 876545678, 987656789, 54321012345, 65432123456, 76543234567, 87654345678, 98765456789, 6543210123456, 7654321234567, 8765432345678, 9876543456789, 765432101234567, 876543212345678, 987654323456789, 87654321012345678, 98765432123456789, 9876543210123456789

Offset: 1

Jaroslav Krizek, Jul 25 2011

For n>9 the structure of digits represents a crater. The first and last digit of each term are identical. The first digits are in consecutive decreasing order. The last digits are in consecutive increasing order. The numbers have only one smallest digit. The number of digits is odd. This sequence is finite with 55 terms. The final term is 9876543210123456789.
Finite subset of primes of this sequence: 2, 3, 5, 7, 101, 7654567.
There are 11 - k terms with 2*k - 1 digits. - Omar E. Pol, Aug 04 2011

			Illustration using a(32)=7654567:
  7  .  .  .  .  .  7
  .  6  .  .  .  6  .
  .  .  5  .  5  .  .
  .  .  .  4  .  .  .

Subset of palindromes (A002113), A193412 and valley numbers (A193413).

Cf. A134810, A134970. - Omar E. Pol, Aug 04 2011

Flatten[Table[FromDigits/@(Join[Reverse[Rest[#]],#]&/@Partition[ Range[ 0,9],n,1]),{n,10}]] (* Harvey P. Dale, Dec 27 2018 *)

ups = [tuple(range(i, j)) for i in range(10) for j in range(i+1, 11)]
afull = sorted(int("".join(map(str, u[::-1] + u[1:]))) for u in ups)
print(afull) # Michael S. Branicky, Aug 02 2022

Corrected and extended by Jaroslav Krizek, Jul 27 2011

cp's OEIS Frontend

A193413 Valley numbers.

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