A141837 a(n) = first term that can be reduced in n steps via repeated interpretation of a(n) as a base b+1 number where b is the largest digit of a(n), such that b is always 3 so that each interpretation is base 4. Terms already fully reduced (i.e., single digits) are excluded.

13, 31, 133, 120332323, 13023002000203

Offset: 1

Author

Chuck Seggelin (seqfan(AT)plastereddragon.com), Jul 10 2008

Keywords

• base
• more
• nonn

Comments

It is possible to compute additional terms by taking the last term, treating it as base-10 and converting to base-4. This will necessarily create a term which can converted back to base 10 yielding the previous term in the sequence which will itself yield N further terms. But there is no guarantee (except in base 2) that the term so derived will be the first term to produce a sequence of N+1 terms. There could be another, smaller, term which satisfies that requirement but which uses different terms. Pushing the last term of this sequence yields 13023002000203 as a possible next term.

Examples

			a(3) = 133 because 133 is the first number that can produce a sequence of three terms by repeated interpretation as a base 4 number: [133] (base-4) --> [31] (base-4) --> [13] (base-4) --> [7]. Since 7 cannot be interpreted as a base 4 number, the sequence terminates with 13. a(1) = 13 because 13 is the first number that can be reduced once, yielding no further terms interpretable as base 4.
		

Crossrefs

Cf. A091049, A141836, A141838, A141839, A141840, A141841, A141842.

Extensions

a(5) from Giovanni Resta, Feb 23 2013