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A193409
Crater numbers.
2
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
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
KEYWORD
base,fini,full,nonn
AUTHOR
Jaroslav Krizek, Jul 25 2011
EXTENSIONS
Corrected and extended by Jaroslav Krizek, Jul 27 2011
STATUS
approved