

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
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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(m1)*(sum(k>0, floor(n/m^k))=n(m1)*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(n1)+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



