cp's OEIS Frontend

A193409 Crater numbers.

%I A193409 #36 Aug 03 2022 02:38:19
%S A193409 0,1,2,3,4,5,6,7,8,9,101,212,323,434,545,656,767,878,989,21012,32123,
%T A193409 43234,54345,65456,76567,87678,98789,3210123,4321234,5432345,6543456,
%U A193409 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 A193409 Crater numbers.
%C A193409 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 A193409 Finite subset of primes of this sequence: 2, 3, 5, 7, 101, 7654567.
%C A193409 There are 11 - k terms with 2*k - 1 digits. - _Omar E. Pol_, Aug 04 2011
%e A193409 Illustration using a(32)=7654567:
%e A193409   7  .  .  .  .  .  7
%e A193409   .  6  .  .  .  6  .
%e A193409   .  .  5  .  5  .  .
%e A193409   .  .  .  4  .  .  .
%t A193409 Flatten[Table[FromDigits/@(Join[Reverse[Rest[#]],#]&/@Partition[ Range[ 0,9],n,1]),{n,10}]] (* _Harvey P. Dale_, Dec 27 2018 *)
%o A193409 (Python)
%o A193409 ups = [tuple(range(i, j)) for i in range(10) for j in range(i+1, 11)]
%o A193409 afull = sorted(int("".join(map(str, u[::-1] + u[1:]))) for u in ups)
%o A193409 print(afull) # _Michael S. Branicky_, Aug 02 2022
%Y A193409 Subset of palindromes (A002113), A193412 and valley numbers (A193413).
%Y A193409 Cf. A134810, A134970. - _Omar E. Pol_, Aug 04 2011
%K A193409 base,fini,full,nonn
%O A193409 1,3
%A A193409 _Jaroslav Krizek_, Jul 25 2011
%E A193409 Corrected and extended by _Jaroslav Krizek_, Jul 27 2011