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A053828
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Sum of digits of (n written in base 7).
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28
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0, 1, 2, 3, 4, 5, 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, 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
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OFFSET
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0,3
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COMMENTS
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Also the fixed point of the morphism 0->{0,1,2,3,4,5,6}, 1->{1,2,3,4,5,6,7}, 2->{2,3,4,5,6,7,8}, etc. - Robert G. Wilson v, Jul 27 2006
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LINKS
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Indranil Ghosh, Table of n, a(n) for n = 0..10000
Jeffrey O. Shallit, Problem 6450, Advanced Problems, The American Mathematical Monthly, Vol. 91, No. 1 (1984), pp. 59-60; Two series, solution to Problem 6450, ibid., Vol. 92, No. 7 (1985), pp. 513-514.
Robert Walker, Self Similar Sloth Canon Number Sequences.
Eric Weisstein's World of Mathematics, Digit Sum.
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FORMULA
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From Benoit Cloitre, Dec 19 2002: (Start)
a(0) = 0, a(7n+i) = a(n) + i for 0 <= i <= 6.
a(n) = n - 6*(Sum_{k>0} floor(n/7^k)) = n - 6*A054896(n). (End)
a(n) = A138530(n,7) for n > 6. - Reinhard Zumkeller, Mar 26 2008
a(n) = Sum_{k>=0} A031007(n,k). - Philippe Deléham, Oct 21 2011
a(0) = 0; a(n) = a(n - 7^floor(log_7(n))) + 1. - Ilya Gutkovskiy, Aug 24 2019
Sum_{n>=1} a(n)/(n*(n+1)) = 7*log(7)/6 (Shallit, 1984). - Amiram Eldar, Jun 03 2021
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EXAMPLE
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a(20) = 2 + 6 = 8 because 20 = 26_7.
From Omar E. Pol, Feb 21 2010: (Start)
It appears that this can be written as a triangle (see the conjecture in the entry A000120):
0,
1,2,3,4,5,6,
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,
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,...
where the rows converge to A173527. (End)
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MATHEMATICA
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Table[Plus @@ IntegerDigits[n, 7], {n, 0, 100}] (* or *)
Nest[ Flatten[ #1 /. a_Integer -> Table[a + i, {i, 0, 6}]] &, {0}, 4] (* Robert G. Wilson v, Jul 27 2006 *)
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PROG
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(PARI) a(n)=if(n<1, 0, if(n%7, a(n-1)+1, a(n/7)))
(PARI) a(n) = my(d=digits(n, 7)); vecsum(d); \\ Michel Marcus, Jan 07 2017
(Magma) [&+Intseq(n, 7): n in [0..100]]; // Vincenzo Librandi, Jan 03 2020
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CROSSREFS
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Cf. A000120, A007953, A231676, A231677, A231678, A231679.
Cf. A173527. - Omar E. Pol, Feb 21 2010
Sequence in context: A338480 A234533 A338495 * A033927 A104414 A279049
Adjacent sequences: A053825 A053826 A053827 * A053829 A053830 A053831
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KEYWORD
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base,nonn
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AUTHOR
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Henry Bottomley, Mar 28 2000
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STATUS
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approved
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