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A182402 Total number of digits in n-th row of a triangle formed by the positive integers. 2
1, 2, 3, 5, 10, 12, 14, 16, 18, 20, 22, 24, 26, 34, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99, 102, 105, 108, 111, 114, 117, 120, 123, 126, 129, 132, 171, 184, 188, 192, 196, 200, 204, 208, 212, 216, 220, 224, 228, 232 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Sequence is nonlinear at each decade transition; for example, row-5 transitions from single-digit (7) to double-digit (10) where sequence jumps (3) to (5); row-14 transitions from 2-digit (92) to 3-digit (105) where sequence jumps from (26) to (34).

The rows of nonlinearity are given by A068092. - Jon Perry, May 26 2013

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A058183(A000217(n)) - A058183(A000217(n-1)), n >= 2. - Omar E. Pol, Jun 25 2012

EXAMPLE

1; .................... (row 1 contains 1 digit)

2,   3; ............... (row 2 contains 2 digits)

4,   5,  6; ........... (row 3 contains 3 digits)

7,   8,  9, 10; ....... (row 4 contains 5 digits)

11, 12, 13, 14, 15; ... (row 5 contains 10 digits)

MATHEMATICA

f[n_] := Length@ Flatten[ IntegerDigits[ Range[n (n - 1)/2 + 1, n (n + 1)/2]]]; Array[f, 58] (* Robert G. Wilson v, Sep 04 2013 *)

PROG

(Haskell)

a182402 n = a182402_list !! (n-1)

a182402_list = map (sum . map a055642) $ t 1 [1..] where

   t i xs = ys : t (i + 1) zs where

     (ys, zs) = splitAt i xs

-- Reinhard Zumkeller, May 26 2013

CROSSREFS

Cf. A055642, A226029 (first differences).

Cf. A068092.

Sequence in context: A002263 A249991 A039022 * A079251 A171785 A050051

Adjacent sequences:  A182399 A182400 A182401 * A182403 A182404 A182405

KEYWORD

nonn,base

AUTHOR

Dave Durgin, Jun 19 2012

EXTENSIONS

Better definition from Omar E. Pol, Jun 25 2012

STATUS

approved

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Last modified March 20 21:49 EDT 2019. Contains 321352 sequences. (Running on oeis4.)