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A127330 Begin with the empty sequence and a starting number s = 0. At step k (k >= 1) append the k consecutive numbers s to s+k-1 and change the starting number (for the next step) to 2s+2. 5
0, 2, 3, 6, 7, 8, 14, 15, 16, 17, 30, 31, 32, 33, 34, 62, 63, 64, 65, 66, 67, 126, 127, 128, 129, 130, 131, 132, 254, 255, 256, 257, 258, 259, 260, 261, 510, 511, 512, 513, 514, 515, 516, 517, 518, 1022, 1023, 1024, 1025, 1026, 1027, 1028, 1029, 1030, 1031, 2046 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

From a TV show.

A129142 and A129143 are similar, slightly more natural, but for a puzzle perhaps too transparent sequences.

Can be seen as a triangle (row by step) read by rows: T(n,k) = T(n-1,k) + 2^n for k < n and T(n,n) = T(n-1,n-1) + 2^n + 1. - Reinhard Zumkeller, Nov 16 2013

LINKS

Reinhard Zumkeller, Rows n = 0..125 of triangle, flattened

EXAMPLE

In step 1 starting number 0 is appended to the empty sequence and the next starting number is 2*0 + 2 = 2. In step 2 the two numbers 2, 3 are appended and the starting number is changed to 2*2 + 2 = 6.

MATHEMATICA

Table[ Range[2^k-2, 2^k+k-3], {k, 1, 11}] // Flatten (* Jean-Fran├žois Alcover, Oct 07 2013, after Klaus Brockhaus *)

Join[{0}, Flatten[With[{nn=10}, Range[#[[1]], Total[#]]&/@Thread[ {Accumulate[ 2^Range[nn]], Range[nn]}]]]] (* Harvey P. Dale, Nov 05 2017 *)

PROG

(PARI) {v=[]; s=0; for(k=1, 11, w=vector(k, j, j+s-1); s=2*s+2; v=concat(v, w)); for(n=1, #v, print1(v[n], ", "))} \\ Klaus Brockhaus, Mar 31 2007

(MAGMA) &cat[ [2^k-2..2^k+k-3]: k in [1..11] ]; // Klaus Brockhaus, Mar 31 2007

(Haskell)

a127330 n k = a127330_tabl !! n !! k

a127330_row n = a127330_tabl !! n

a127330_tabl = step 0 1 where

   step s k = [s .. s + k - 1] : step (2 * s + 2) (k + 1)

-- Reinhard Zumkeller, Nov 16 2013

CROSSREFS

Cf. A129142, A129143.

Cf. A000918 (left edge), A145071 (right edge).

Sequence in context: A166458 A189013 A242940 * A035346 A030164 A066646

Adjacent sequences:  A127327 A127328 A127329 * A127331 A127332 A127333

KEYWORD

easy,nice,nonn,tabl

AUTHOR

Steven Cartier (steven.cartier(AT)rogers.com), Mar 30 2007

EXTENSIONS

Edited and extended by Klaus Brockhaus, Mar 31 2007

Keyword tabl added and offset changed by Reinhard Zumkeller, Nov 16 2013

STATUS

approved

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Last modified September 23 19:41 EDT 2020. Contains 337315 sequences. (Running on oeis4.)