A193409 Crater numbers.

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

Author

Jaroslav Krizek, Jul 25 2011

Keywords

• base
• fini
• full
• nonn

Comments

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

Examples

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

Crossrefs

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

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

Programs

Mathematica

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

Python

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

Extensions

Corrected and extended by Jaroslav Krizek, Jul 27 2011