

A173527


a(n) = 1 + A053828(n1), where A053828 is the sum of digits in base 7.


6



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
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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+n1) 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+n1) 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+b1} 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/(b1); k := ceil(log(k)/log(b)) ; A053828(b^k+n1) ; end if; end proc:
seq(A173527(n), n=1..100) ; # R. J. Mathar, Dec 09 2010


MATHEMATICA

Table[Total[IntegerDigits[n1, 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



