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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

%I #16 Feb 16 2022 23:33:06

%S 0,2,3,6,7,8,14,15,16,17,30,31,32,33,34,62,63,64,65,66,67,126,127,128,

%T 129,130,131,132,254,255,256,257,258,259,260,261,510,511,512,513,514,

%U 515,516,517,518,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,2046

%N 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.

%C From a TV show.

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

%C 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

%H Reinhard Zumkeller, <a href="/A127330/b127330.txt">Rows n = 0..125 of triangle, flattened</a>

%e 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.

%t Table[ Range[2^k-2, 2^k+k-3], {k, 1, 11}] // Flatten (* _Jean-François Alcover_, Oct 07 2013, after _Klaus Brockhaus_ *)

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

%o (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

%o (Magma) &cat[ [2^k-2..2^k+k-3]: k in [1..11] ]; // _Klaus Brockhaus_, Mar 31 2007

%o (Haskell)

%o a127330 n k = a127330_tabl !! n !! k

%o a127330_row n = a127330_tabl !! n

%o a127330_tabl = step 0 1 where

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

%o -- _Reinhard Zumkeller_, Nov 16 2013

%Y Cf. A129142, A129143.

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

%K easy,nice,nonn,tabl

%O 0,2

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

%E Edited and extended by _Klaus Brockhaus_, Mar 31 2007

%E Keyword tabl added and offset changed by _Reinhard Zumkeller_, Nov 16 2013

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