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

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

Offset: 1

Author

Ulrich Schimke (ulrschimke(AT)aol.com)

Keywords

• nonn
• fini
• full
• base
• nice
• eigen

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

• David Wasserman, Table of n, a(n) for n = 1..109 (full sequence)
• Andre Kowacs, Studies on the Pea Pattern Sequence, arXiv:1708.06452 [math.HO], 2017.

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