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A233932 Irregular table read by rows: T(n,k) = binary representation of n shifted right k times and incremented if the last shifted away bit was set. 0
1, 1, 1, 2, 1, 2, 1, 1, 3, 1, 1, 3, 2, 1, 4, 2, 1, 4, 2, 1, 1, 5, 2, 1, 1, 5, 3, 1, 1, 6, 3, 1, 1, 6, 3, 2, 1, 7, 3, 2, 1, 7, 4, 2, 1, 8, 4, 2, 1, 8, 4, 2, 1, 1, 9, 4, 2, 1, 1, 9, 5, 2, 1, 1, 10, 5, 2, 1, 1, 10, 5, 3, 1, 1, 11, 5, 3, 1, 1, 11, 6, 3, 1, 1, 12, 6, 3, 1, 1, 12, 6, 3, 2, 1, 13, 6, 3, 2, 1, 13, 7, 3, 2, 1, 14, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

The last shifted away bit is the (k-1)-th bit from the right.

The length of the n-th row is A070939(n).

Terms in the n-th row add to n.

LINKS

Table of n, a(n) for n=1..106.

Index entries for sequences related to binary expansion of n

FORMULA

T(n,k) = round(n/2^k), 1 <= k <= floor(log_2(n)) + 1, where round(1/2)=1. - Ridouane Oudra, Sep 02 2019

EXAMPLE

22 in binary is 10110, so the row length is 5. T(22, 1) = 11, T(22, 2) = 5 + 1 = 6, T(22, 3) = 2 + 1 = 3, T(22, 4) = 1, T(22, 5) = 0 + 1. So the 22nd row reads 11, 6, 3, 1, 1.

Table starts:

1,

1,1,

2,1,

2,1,1,

3,1,1,

3,2,1,

4,2,1,

4,2,1,1,

5,2,1,1,

5,3,1,1,

...

PROG

(PARI) T(n, k)=b=binary(n); n\2^k+b[#b-k+1]

(PARI) row(n) = my(b=binary(n)); vector(#b, k, n\2^k+b[#b-k+1]); \\ Michel Marcus, Sep 03 2019

CROSSREFS

Cf. A120385.

Sequence in context: A249809 A075104 A253667 * A008289 A326625 A188884

Adjacent sequences:  A233929 A233930 A233931 * A233933 A233934 A233935

KEYWORD

nonn,tabf,changed

AUTHOR

Ralf Stephan, Dec 18 2013

STATUS

approved

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Last modified September 16 02:16 EDT 2019. Contains 327088 sequences. (Running on oeis4.)