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

1,3

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

Links

Table of n, a(n) for n=1..55.

Example

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

Mathematica

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

Prog

(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

Crossrefs

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

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

Sequence in context: A193412 A266139 A154562 * A280823 A367342 A302656

Adjacent sequences: A193406 A193407 A193408 * A193410 A193411 A193412

Keyword

base,fini,full,nonn

Author

Jaroslav Krizek, Jul 25 2011

Extensions

Corrected and extended by Jaroslav Krizek, Jul 27 2011

Status

approved