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A053828
Sum of digits of (n written in base 7).
29
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
OFFSET
0,3
COMMENTS
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
LINKS
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.
Eric Weisstein's World of Mathematics, Digit Sum.
FORMULA
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
EXAMPLE
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)
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
Cf. A173527. - Omar E. Pol, Feb 21 2010
Sequence in context: A338480 A234533 A338495 * A033927 A104414 A279049
KEYWORD
base,nonn
AUTHOR
Henry Bottomley, Mar 28 2000
STATUS
approved