A173527 a(n) = 1 + A053828(n-1), where A053828 is the sum of digits in base 7.

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, 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, 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

Offset: 1

Author

Omar E. Pol, Feb 20 2010

Keywords

• nonn
• base

Comments

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.

See conjecture in the entry A000120.

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.

Crossrefs

Cf. A000120, A053828, A063787.

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

Programs

Maple

A053828 := proc(n) add(d, d=convert(n,base,7)) ; end proc:
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:
seq(A173527(n),n=1..100) ; # R. J. Mathar, Dec 09 2010

Mathematica

Table[Total[IntegerDigits[n-1,7]]+1,{n,110}] (* Harvey P. Dale, Apr 01 2018 *)

Formula

a(n) = A053828(7^k+n-1) where k >= ceiling(log_7(n/6)). [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=7. [Joerg Arndt, Dec 08 2010]

Extensions

More terms from Vincenzo Librandi, Feb 21 2010