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G. C. Greubel, <a href="/A173526/b173526.txt">Table of n, a(n) for n = 1..10000</a>
a(n) = A053827(6^k+n-1) where k >= ceiling(log_6(n/5)). [_- _R. J. Mathar_, Dec 09 2010]
j->{j,j+1,...,j+b-1} for b=6. [_- _Joerg Arndt_, Dec 08 2010]
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
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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. .
This here 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.
a(n) = A053827(6^k+n-1) where k >= ceilceiling( 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]
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More terms from _Vincenzo Librandi (vincenzo.librandi(AT)tin.it), _, Aug 02 2010
_Omar E. Pol (info(AT)polprimos.com), _, Feb 20 2010