A173527 - OEIS

%I #17 May 12 2019 03:04:26

%S 1,2,3,4,5,6,7,2,3,4,5,6,7,8,3,4,5,6,7,8,9,4,5,6,7,8,9,10,5,6,7,8,9,

%T 10,11,6,7,8,9,10,11,12,7,8,9,10,11,12,13,2,3,4,5,6,7,8,3,4,5,6,7,8,9,

%U 4,5,6,7,8,9,10,5,6,7,8,9,10,11,6,7,8,9,10,11,12,7,8,9,10,11,12,13,8,9,10,11,12,13,14,3,4

%N a(n) = 1 + A053828(n-1), where A053828 is the sum of digits in base 7.

%C If A053828 is regarded as a triangle then the rows converge to this sequence, i.e., a(n) = A053828(7^k+n-1) in the limit k->infinity, where k plays the role of a row index in A053828.

%C See conjecture in the entry A000120.

%C This is the case for base b=7 for the sum of digits. A063787 and A173523 to A173526 deal with the bases 2 to 6. A173525 contains generic remarks concerning these 8 sequences which look in equivalent ways at their sum of digits as a sequence with triangular structure.

%F a(n) = A053828(7^k+n-1) where k >= ceiling(log_7(n/6)). [_R. J. Mathar_, Dec 09 2010]

%F 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=7. [_Joerg Arndt_, Dec 08 2010]

%p A053828 := proc(n) add(d, d=convert(n,base,7)) ; end proc:

%p A173527 := proc(n) local b; b := 7 ; if n < b then n; else k := n/(b-1); k := ceil(log(k)/log(b)) ; A053828(b^k+n-1) ; end if; end proc:

%p seq(A173527(n),n=1..100) ; # _R. J. Mathar_, Dec 09 2010

%t Table[Total[IntegerDigits[n-1,7]]+1,{n,110}] (* _Harvey P. Dale_, Apr 01 2018 *)

%Y Cf. A000120, A053828, A063787.

%Y Cf. A173523, A173524, A173525, A173526, A173528, A173529.

%K nonn,base

%O 1,2

%A _Omar E. Pol_, Feb 20 2010

%E More terms from _Vincenzo Librandi_, Feb 21 2010