A141840 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 6 so that each interpretation is base 7. Terms already fully reduced (i.e., single digits) are excluded.

16, 64, 631, 1561, 4360, 15466, 63043, 34406005, 565306024, 23001126626004, 4562530234315632

Offset: 1

Author

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

Keywords

• base
• more
• nonn

Comments

It is sometimes possible to compute additional terms by taking the last term, treating it as base 10 and converting to base 7. This may create a term minimally interpretable as base 7 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 does not produce a value minimally interpretable as base 7.

Examples

			a(3) = 631 because 631 is the first number that can produce a sequence of three terms by repeated interpretation as a base 7 number: [631] (base-7) --> [316] (base-7) --> [160] (base-7) --> [91]. Since 91 cannot be minimally interpreted as a base 7 number, the sequence terminates with 160. a(1) = 16 because 16 is the first number that can be reduced once, yielding no further terms minimally interpretable as base 7.
		

Crossrefs

Cf. A091049, A141836, A141837, A141838, A141839, A141841, A141842.

Extensions

a(10)-a(11) from Giovanni Resta, Feb 23 2013