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.

A047841 Autobiographical numbers: Fixed under operator T (A047842): "Say what you see".

Original entry on oeis.org

22, 10213223, 10311233, 10313314, 10313315, 10313316, 10313317, 10313318, 10313319, 21322314, 21322315, 21322316, 21322317, 21322318, 21322319, 31123314, 31123315, 31123316, 31123317, 31123318, 31123319
Offset: 1

Views

Author

Ulrich Schimke (ulrschimke(AT)aol.com)

Keywords

Comments

A digit count numerically summarizes the frequency of digits 0 through 9 in that order when they occur in a number.
This uses a different method from A108810. Here the digits are described in increasing order, whereas in A108810 they can be described in any order.
This sequence is finite, since T(x) < x for every x with at least 22 digits. Last term is a(109) = 101112213141516171819. - Schimke
A character in the Verghese (2009) novel declares that 10213223 "is the only number that describes itself when you read it." - Alonso del Arte, Jan 26 2014

Examples

			10313314 contains 1 0's, 3 1's, 3 3's and 1 4's, hence T(10313314) = 10313314 is in the sequence
The entry 3122331418, for instance, is a member since it is indeed made up of three 1's, two 2's, three 3's, one 4 and one 8.

References

  • J. N. Kapur, Reflections of a Mathematician, Chapter 33, pp. 314-318, Arya Book Depot, New Delhi 1996.
  • Abraham Verghese, Cutting for Stone: A Novel. New York: Alfred A. Knopf (2009): 294.

Links

Crossrefs

Cf. A005151, which is the sequence 1, T(1), T(T(1)), .. ending in the fixed-point 21322314.
Cf. A104785, A104786, A104787, A108810.

Extensions

Entry revised by N. J. A. Sloane, Dec 15 2006

A104786 a(n) = least member of A047841 with n digits, or 0 if no such number exists.

Original entry on oeis.org

0, 22, 0, 0, 0, 0, 0, 10213223, 0, 1031223314, 0, 0, 0, 10413223241516, 0, 1051322314251617, 0, 106132231415261718, 1011112131415161718, 10713223141516271819, 101112213141516171819
Offset: 1

Views

Author

Lekraj Beedassy, Mar 25 2005

Keywords

Crossrefs

Cf. A047841, A104785, A104787, A039616, A039617.

Extensions

Edited by David Wasserman, Apr 17 2008

A104787 a(n) = greatest member of A047841 with n digits, or 0 if no such number exists.

Original entry on oeis.org

0, 22, 0, 0, 0, 0, 0, 31331819, 0, 3122331819, 0, 0, 0, 41322324171819, 0, 5132232516171819, 0, 613223141526171819, 1111213141516171819, 10713223141516271819, 101112213141516171819
Offset: 1

Views

Author

Lekraj Beedassy, Mar 25 2005

Keywords

Crossrefs

Cf. A047841, A104785, A104786, A039616, A039617.

Extensions

Edited by David Wasserman, Apr 17 2008

A103618 Number of steps required for n to reach a digit count invariant or cycle loop under the 'Look and Say' function A045918.

Original entry on oeis.org

10, 12, 11, 12, 8, 10, 10, 10, 10, 10, 9, 11, 10, 11, 7, 9, 9, 9, 9, 9, 6, 10, 0, 9, 6, 6, 6, 6, 6, 6, 8, 11, 9, 10, 6, 8, 8, 8, 8, 8, 9, 7, 6, 6, 7, 8, 9, 9, 9, 9, 10, 9, 6, 8, 8, 7, 9, 10, 10, 10, 12, 9, 6, 8, 9, 9, 7, 10, 12, 12, 13, 9, 6, 8, 9, 10, 10, 7, 12, 13, 14, 9, 6, 8, 9, 10, 12, 12, 7, 13
Offset: 1

Views

Author

Lekraj Beedassy, Mar 25 2005

Keywords

Examples

			a(10)=9 because we have the 9-step chain 10 -> 1011 -> 1031 -> 102113 -> 103112113 -> 10411223 -> 1031221314 -> 1041222314 -> 1031321324 -> 1031223314, the latter being autobiographical, hence invariant. Also, a(40)=9 since we have the digit count iteration 40 -> 1014 -> 102114 -> 10311214 -> 1041121314 -> 1051121324 -> 104122131415 -> 105122132415 -> 104132131425 -> 104122232415 <-> 103142132415, ending in a 2-cycle loop.

Links

Crossrefs

Cf. A005151, A047841, A104785, A104786, A104787, A308781 (duplicate?).

Extensions

Corrected and extended by Sean A. Irvine, Feb 08 2010
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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