login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A138530 Triangle read by rows: T(n,k) = sum of digits of n in base k representation, 1<=k<=n. 18
1, 2, 1, 3, 2, 1, 4, 1, 2, 1, 5, 2, 3, 2, 1, 6, 2, 2, 3, 2, 1, 7, 3, 3, 4, 3, 2, 1, 8, 1, 4, 2, 4, 3, 2, 1, 9, 2, 1, 3, 5, 4, 3, 2, 1, 10, 2, 2, 4, 2, 5, 4, 3, 2, 1, 11, 3, 3, 5, 3, 6, 5, 4, 3, 2, 1, 12, 2, 2, 3, 4, 2, 6, 5, 4, 3, 2, 1, 13, 3, 3, 4, 5, 3, 7, 6, 5, 4, 3, 2, 1, 14, 3, 4, 5, 6, 4, 2, 7, 6, 5, 4, 3, 2, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A131383(n) = sum of n-th row;

A000027(n) = T(n,1);

A000120(n) = T(n,2) for n>1;

A053735(n) = T(n,3) for n>2;

A053737(n) = T(n,4) for n>3;

A053824(n) = T(n,5) for n>4;

A053827(n) = T(n,6) for n>5;

A053828(n) = T(n,7) for n>6;

A053829(n) = T(n,8) for n>7;

A053830(n) = T(n,9) for n>8;

A007953(n) = T(n,10) for n>9;

A053831(n) = T(n,11) for n>10;

A053832(n) = T(n,12) for n>11;

A053833(n) = T(n,13) for n>12;

A053834(n) = T(n,14) for n>13;

A053835(n) = T(n,15) for n>14;

A053836(n) = T(n,16) for n>15;

A007395(n) = T(n,n-1) for n>1;

A000012(n) = T(n,n).

LINKS

Alois P. Heinz, Rows n = 1..141, flattened

Eric Weisstein's World of Mathematics, Digit Sum

EXAMPLE

Start of the triangle for n in base k representation:

......................1

....................11....10

......... ........111....11...10

................1111...100...11..10

..............11111...101...12..11..10

............111111...110...20..12..11..10

..........1111111...111...21..13..12..11..10

........11111111..1000...22..20..13..12..11..10

......111111111..1001..100..21..14..13..12..11..10

....1111111111..1010..101..22..20..14..13..12..11..10

..11111111111..1011..102..23..21..15..14..13..12..11..10

111111111111..1100..110..30..22..20..15..14..13..12..11..10,

and the triangle of sums of digits starts:

......................1

.....................2...1

......... ..........3...2...1

...................4...1...2...1

..................5...2...3...2...1

.................6...2...2...3...2...1

................7...3...3...4...3...2...1

...............8...1...4...2...4...3...2...1

..............9...2...1...3...5...4...3...2...1

............10...2...2...4...2...5...4...3...2...1

...........11...3...3...5...3...6...5...4...3...2...1

..........12...2...2...3...4...2...6...5...4...3...2...1.

PROG

(Haskell)

a138530 n k = a138530_tabl !! (n-1) !! (k-1)

a138530_row n = a138530_tabl !! (n-1)

a138530_tabl = zipWith (map . flip q) [1..] a002260_tabl where

   q 1 n = n

   q b n = if n < b then n else q b n' + d where (n', d) = divMod n b

-- Reinhard Zumkeller, Apr 29 2015

CROSSREFS

Cf. A007953. See A240236 for another version.

Cf. A002260.

Sequence in context: A086414 A098896 A108371 * A002341 A128260 A083368

Adjacent sequences:  A138527 A138528 A138529 * A138531 A138532 A138533

KEYWORD

nonn,base,tabl

AUTHOR

Reinhard Zumkeller, Mar 26 2008

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 3 16:24 EST 2016. Contains 278745 sequences.