A173526 - OEIS

%I #17 Jul 02 2019 02:59:30

%S 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,

%T 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,

%U 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

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

%C 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.

%C See conjecture in the entry A000120.

%C 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.

%H G. C. Greubel, <a href="/A173526/b173526.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%F j->{j,j+1,...,j+b-1} for b=6. - _Joerg Arndt_, Dec 08 2010

%t Table[1 + Total[IntegerDigits[n-1, 6]], {n, 1, 110}] (* _G. C. Greubel_, Jul 02 2019 *)

%o (PARI) A053827(n)= if(n<1, 0, if(n%6, a(n-1)+1, a(n/6)));

%o vector(110, n, 1+A053827(n-1)) \\ _G. C. Greubel_, Jul 02 2019

%Y Cf. A000120, A053827, A063787.

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

%K nonn,base

%O 1,2

%A _Omar E. Pol_, Feb 20 2010

%E More terms from _Vincenzo Librandi_, Aug 02 2010