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A053831 Sum of digits of n written in base 11. 4
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 7, 8, 9, 10, 11, 12, 13, 14, 15 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Also the fixed point of the morphism 0->{0,1,2,3,4,5,6,7,8,9,10}, 1->{1,2,3,4,5,6,7,8,9,10,11}, 2->{2,3,4,5,6,7,8,9,10,11,12}, etc. - Robert G. Wilson v, Jul 27 2006

a(n) = A138530(n,11) for n > 10. - Reinhard Zumkeller, Mar 26 2008

LINKS

Table of n, a(n) for n=0..85.

Robert Walker, Self Similar Sloth Canon Number Sequences

Eric Weisstein's World of Mathematics, Digit Sum

FORMULA

a(0)=0, then a(11n+i)=a(n)+i 0<=i<=10; a(n)=n-(m-1)*(sum(k>0, floor(n/m^k))=n-(m-1)*A064458 (n). - Benoit Cloitre, Dec 19 2002

EXAMPLE

a(20) = 1 + 9 = 10 because 20 is written as 19 base 11.

MATHEMATICA

Table[Plus @@ IntegerDigits[n, 11], {n, 0, 86}] (* or *)

Nest[ Flatten[ #1 /. a_Integer -> Table[a + i, {i, 0, 10}]] &, {0}, 2] (* Robert G. Wilson v, Jul 27 2006 *)

PROG

(PARI) a(n)=if(n<1, 0, if(n%11, a(n-1)+1, a(n/11)))

CROSSREFS

Cf. A000120, A007953.

Sequence in context: A190599 A214587 A010889 * A263131 A274206 A214949

Adjacent sequences:  A053828 A053829 A053830 * A053832 A053833 A053834

KEYWORD

base,nonn

AUTHOR

Henry Bottomley, Mar 28 2000

STATUS

approved

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Last modified October 20 18:08 EDT 2018. Contains 316401 sequences. (Running on oeis4.)