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%I #36 Aug 03 2022 02:38:19
%S 0,1,2,3,4,5,6,7,8,9,101,212,323,434,545,656,767,878,989,21012,32123,
%T 43234,54345,65456,76567,87678,98789,3210123,4321234,5432345,6543456,
%U 7654567,8765678,9876789,432101234,543212345,654323456,765434567,876545678,987656789,54321012345,65432123456,76543234567,87654345678,98765456789,6543210123456,7654321234567,8765432345678,9876543456789,765432101234567,876543212345678,987654323456789,87654321012345678,98765432123456789,9876543210123456789
%N Crater numbers.
%C 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.
%C Finite subset of primes of this sequence: 2, 3, 5, 7, 101, 7654567.
%C There are 11 - k terms with 2*k - 1 digits. - _Omar E. Pol_, Aug 04 2011
%e Illustration using a(32)=7654567:
%e 7 . . . . . 7
%e . 6 . . . 6 .
%e . . 5 . 5 . .
%e . . . 4 . . .
%t Flatten[Table[FromDigits/@(Join[Reverse[Rest[#]],#]&/@Partition[ Range[ 0,9],n,1]),{n,10}]] (* _Harvey P. Dale_, Dec 27 2018 *)
%o (Python)
%o ups = [tuple(range(i, j)) for i in range(10) for j in range(i+1, 11)]
%o afull = sorted(int("".join(map(str, u[::-1] + u[1:]))) for u in ups)
%o print(afull) # _Michael S. Branicky_, Aug 02 2022
%Y Subset of palindromes (A002113), A193412 and valley numbers (A193413).
%Y Cf. A134810, A134970. - _Omar E. Pol_, Aug 04 2011
%K base,fini,full,nonn
%O 1,3
%A _Jaroslav Krizek_, Jul 25 2011
%E Corrected and extended by _Jaroslav Krizek_, Jul 27 2011
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