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

1,2

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.

Links

Table of n, a(n) for n=1..100.

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]

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 *)

Crossrefs

Cf. A000120, A053828, A063787.

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

Sequence in context: A165111 A038387 A240832 * A043267 A167514 A091733

Adjacent sequences: A173524 A173525 A173526 * A173528 A173529 A173530

Keyword

nonn,base

Author

Omar E. Pol, Feb 20 2010

Extensions

More terms from Vincenzo Librandi, Feb 21 2010

Status

approved