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A138530 Triangle read by rows: T(n,k) = sum of digits of n in base k representation, 1<=k<=n. 23
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.

MATHEMATICA

T[n_, k_] := If[k == 1, n, Total[IntegerDigits[n, k]]];

Table[T[n, k], {n, 1, 14}, {k, 1, n}] // Flatten (* Jean-François Alcover, Oct 25 2021 *)

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 A348888 A128260

Adjacent sequences: A138527 A138528 A138529 * A138531 A138532 A138533

KEYWORD

nonn,base,tabl

AUTHOR

Reinhard Zumkeller, Mar 26 2008

STATUS

approved

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Last modified December 7 15:01 EST 2022. Contains 358667 sequences. (Running on oeis4.)