cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A193409 Crater numbers.

Original entry on oeis.org

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

Views

Author

Jaroslav Krizek, Jul 25 2011

Keywords

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

A193412 1..9 followed by the canyon numbers A134970.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 101, 202, 212, 303, 313, 323, 404, 414, 424, 434, 505, 515, 525, 535, 545, 606, 616, 626, 636, 646, 656, 707, 717, 727, 737, 747, 757, 767, 808, 818, 828, 838, 848, 858, 868, 878, 909, 919, 929, 939, 949, 959, 969, 979, 989, 2012
Offset: 1

Views

Author

Jaroslav Krizek, Jul 25 2011

Keywords

Comments

For n > 9 the structure of digits represents an abyss. The first digit is equal to the last digit (1 - 9). The first digits are in decreasing order. The last digits are in increasing order. The numbers only have one smallest digit. This sequence is finite. The final term is 9876543210123456789.
Superset of crater numbers (A193409). Subset of valley numbers (A193413).

Examples

			Illustration using 654356:
  6  .  .  .  .  6
  .  5  .  .  5  .
  .  .  4  .  .  .
  .  .  .  3  .  .

Crossrefs

Cf. A193409, A193413, A134970.

A193414 Numbers m such that written in base 2 the structure of digits represents a valley.

Original entry on oeis.org

1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 23, 25, 27, 29, 31, 33, 35, 39, 47, 49, 51, 55, 57, 59, 61, 63, 65, 67, 71, 79, 95, 97, 99, 103, 111, 113, 115, 119, 121, 123, 125, 127, 129, 131, 135, 143, 159, 191, 193, 195, 199, 207, 223, 225, 227, 231, 239, 241, 243
Offset: 1

Views

Author

Jaroslav Krizek, Jul 25 2011

Keywords

Comments

For n > 1 the structure of digits of numbers written in base 2 represents a valley. The first digit is equal to the last digit (1). The first digits are in nonincreasing order. The last digits are in nondecreasing order. The numbers may have more than one 0 digit. Sequence is infinite.
See A193415: numbers m written in base 2: {1, 11, 101, 111, 1001, 1011, 1101, 1111, ...}.

Examples

			Illustration using 67 = 1000011_2:
  1  .  .  .  .  1  1
  .  0  0  0  0  .  .

Crossrefs

Cf. A193413 (Valley numbers written in base 10), A193415.

Programs

  • Mathematica
    Select[Range[300], MemberQ[{1, 3}, Length[Split[IntegerDigits[#, 2]]]] &] (* T. D. Noe, Jul 26 2011 *)

Extensions

First term corrected by Jaroslav Krizek, Jul 27 2011

A193415 Numbers from A193414 written in base 2.

Original entry on oeis.org

1, 11, 101, 111, 1001, 1011, 1101, 1111, 10001, 10011, 10111, 11001, 11011, 11101, 11111, 100001, 100011, 100111, 101111, 110001, 110011, 110111, 111001, 111011, 111101, 111111, 1000001, 1000011, 1000111, 1001111, 1011111, 1100001, 1100011, 1100111, 1101111
Offset: 1

Views

Author

Jaroslav Krizek, Jul 25 2011

Keywords

Comments

For n > 1 the structure of digits represents a valley. The first digit is equal to the last digit (1). The first digits are in nonincreasing order. The last digits are in nondecreasing order. The numbers may have more than one 0 digit. Sequence is infinite.

Examples

			Illustration using 67 = 1000011_2:
  1  .  .  .  .  1  1
  .  0  0  0  0  .  .

Crossrefs

Cf. A193413 (Valley numbers written in base 10).
Showing 1-4 of 4 results.

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