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A053828 Sum of digits of (n written in base 7). 19

%I

%S 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,

%T 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,

%U 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

%N Sum of digits of (n written in base 7).

%C 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

%C a(n) = A138530(n,7) for n > 6. - _Reinhard Zumkeller_, Mar 26 2008

%H Indranil Ghosh, <a href="/A053828/b053828.txt">Table of n, a(n) for n = 0..10000</a>

%H Robert Walker, <a href="http://robertinventor.com/ftswiki/Self_Similar_Sloth_Canon_Number_Sequences">Self Similar Sloth Canon Number Sequences</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DigitSum.html">Digit Sum</a>

%F From _Benoit Cloitre_, Dec 19 2002: (Start)

%F a(0)=0, a(7n+i) = a(n) + i for 0 <= i <= 6;

%F a(n) = n - 6*(Sum_{k>0} floor(n/7^k)) = n - 6*A054896(n). (End)

%F a(n) = Sum_{k>=0} A031007(n,k). - _Philippe Deléham_, Oct 21 2011

%e a(20) = 2 + 6 = 8 because 20 = 26_7.

%e From _Omar E. Pol_, Feb 21 2010: (Start)

%e It appears that this can be written as a triangle (see the conjecture in the entry A000120):

%e 0,

%e 1,2,3,4,5,6,

%e 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,

%e 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,...

%e where the rows converge to A173527. (End)

%t Table[Plus @@ IntegerDigits[n, 7], {n, 0, 100}] (* or *)

%t Nest[ Flatten[ #1 /. a_Integer -> Table[a + i, {i, 0, 6}]] &, {0}, 4] (* _Robert G. Wilson v_, Jul 27 2006 *)

%o (PARI) a(n)=if(n<1,0,if(n%7,a(n-1)+1,a(n/7)))

%o (PARI) a(n) = my(d=digits(n, 7)); vecsum(d); \\ _Michel Marcus_, Jan 07 2017

%Y Cf. A000120, A007953, A231676-A231679.

%Y Cf. A173527. - _Omar E. Pol_, Feb 21 2010

%K base,nonn

%O 0,3

%A _Henry Bottomley_, Mar 28 2000

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Last modified August 24 18:12 EDT 2019. Contains 326295 sequences. (Running on oeis4.)