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 A053828 Sum of digits of (n written in base 7). 20
 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 (list; graph; refs; listen; history; text; internal format)
 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 a(n) = A138530(n,7) for n > 6. - Reinhard Zumkeller, Mar 26 2008 LINKS Indranil Ghosh, Table of n, a(n) for n = 0..10000 Robert Walker, Self Similar Sloth Canon Number Sequences 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) = 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 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. A000120, A007953, A231676-A231679. Cf. A173527. - Omar E. Pol, Feb 21 2010 Sequence in context: A053842 A010885 A234533 * A033927 A104414 A279049 Adjacent sequences:  A053825 A053826 A053827 * A053829 A053830 A053831 KEYWORD base,nonn AUTHOR Henry Bottomley, Mar 28 2000 STATUS approved

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Last modified August 12 03:34 EDT 2020. Contains 336436 sequences. (Running on oeis4.)