A173526 - OEIS

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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

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OFFSET

1,2

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

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

MATHEMATICA

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

PROG

(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

CROSSREFS