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A173527 a(n) = 1+A053828(n-1), where A053828 is the sum-of-digits in base 7. 4
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 (list; graph; refs; listen; history; text; internal format)
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>= ceil( 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

CROSSREFS

Cf. A000120, A053828, A063787, A173523 - 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

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Last modified July 21 04:27 EDT 2017. Contains 289632 sequences.