A173526 a(n) = 1 + A053827(n-1), where A053827 is the sum-of-digits function in base 6.

1, 2, 3, 4, 5, 6, 2, 3, 4, 5, 6, 7, 3, 4, 5, 6, 7, 8, 4, 5, 6, 7, 8, 9, 5, 6, 7, 8, 9, 10, 6, 7, 8, 9, 10, 11, 2, 3, 4, 5, 6, 7, 3, 4, 5, 6, 7, 8, 4, 5, 6, 7, 8, 9, 5, 6, 7, 8, 9, 10, 6, 7, 8, 9, 10, 11, 7, 8, 9, 10, 11, 12, 3, 4, 5, 6, 7, 8, 4, 5, 6, 7, 8, 9, 5, 6, 7, 8, 9, 10, 6, 7, 8, 9, 10, 11, 7, 8, 9, 10

Offset: 1

Author

Omar E. Pol, Feb 20 2010

Keywords

• nonn
• base

Comments

If A053827 is regarded as a triangle then the rows converge to this sequence, i.e., a(n) = A053827(6^k+n-1) in the limit k->infinity, where k plays the role of a row index in A053827.

See conjecture in the entry A000120.

This sequence is the base b=6 case equivalent to A063787 (b=2), A173523 (b=3), A173524 (b=4), A173525 (b=5). Generic comments concerning the various bases are in A173525.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000120, A053827, A063787.

Cf. A173523, A173524, A173525, A173527, A173528, A173529.

Programs

Mathematica

Table[1 + Total[IntegerDigits[n-1, 6]], {n, 1, 110}] (* G. C. Greubel, Jul 02 2019 *)

PARI

A053827(n)= if(n<1, 0, if(n%6, a(n-1)+1, a(n/6)));
vector(110, n, 1+A053827(n-1)) \\ G. C. Greubel, Jul 02 2019

Formula

a(n) = A053827(6^k+n-1) where k >= ceiling(log_6(n/5)). - R. J. Mathar, Dec 09 2010

Conjecture: Fixed point of the morphism 1->{1,2,3,...,b}, 2->{2,3,4,...,b+1},

j->{j,j+1,...,j+b-1} for b=6. - Joerg Arndt, Dec 08 2010

Extensions

More terms from Vincenzo Librandi, Aug 02 2010