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A067255 Irregular triangle read by rows: row n gives exponents in prime factorization of n. 15
0, 1, 0, 1, 2, 0, 0, 1, 1, 1, 0, 0, 0, 1, 3, 0, 2, 1, 0, 1, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 4, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 1, 0, 0, 2, 1, 0, 0, 0, 0, 1, 0, 3, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Lengths of the runs are given by A061395(n),n>=2: [1,2,1,3,2,4,1,2,... ].

This sequence contains every finite sequence of nonnegative integers. - Franklin T. Adams-Watters, Jun 22 2005

LINKS

Reinhard Zumkeller, Rows n = 1..250 of triangle, flattened

Jeppe Stig Nielsen, See this explanation.

EXAMPLE

1 = 2^0

2 = 2^1

3 = 2^0 3^1

4 = 2^2

5 = 2^0 3^0 5^1

6 = 2^1 3^1

... and reading the exponents gives the sequence.

Since for example 99=2^0*3^2*5^0*7^0*11^1, we use this symbol for ninety-nine: 99: {0,2,0,0,1}. Concatenating all the symbols for 1,2,3,4,5,6,..., we get the sequence.

PROG

(Haskell)

a067255 n k = a067255_tabf !! (n-1) !! (k-1)

a067255_row 1 = [0]

a067255_row n = f n a000040_list where

   f 1 _      = []

   f u (p:ps) = g u 0 where

     g v e = if m == 0 then g v' (e + 1) else e : f v ps

             where (v', m) = divMod v p

a067255_tabf = map a067255_row [1..]

-- Reinhard Zumkeller, Jun 11 2013

CROSSREFS

Cf. A133457.

Cf. A001222, which gives the row sums of this table.

For another version see A143078.

Cf. A007814 (left edge), A071178 (right edge).

Cf. A082786 (same as regular triangle).

Sequence in context: A216654 A029429 A064559 * A065716 A079409 A114643

Adjacent sequences:  A067252 A067253 A067254 * A067256 A067257 A067258

KEYWORD

easy,nonn,tabf

AUTHOR

Jeppe Stig Nielsen, Feb 20 2002

STATUS

approved

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Last modified December 16 07:41 EST 2017. Contains 296076 sequences.