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A122872 Table by antidiagonals, T(n,k) is k-th number that starts with n in binary representation. 0
1, 2, 2, 3, 4, 3, 4, 5, 6, 4, 5, 8, 7, 8, 5, 6, 9, 12, 9, 10, 6, 7, 10, 13, 16, 11, 12, 7, 8, 11, 14, 17, 20, 13, 14, 8, 9, 16, 15, 18, 21, 24, 15, 16, 9, 10, 17, 24, 19, 22, 25, 28, 17, 18, 10, 11, 18, 25, 32, 23, 26, 29, 32, 19, 20, 11, 12, 19, 26, 33, 40, 27, 30, 33, 36, 21, 22, 12 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

In rows n through 2n-1, every integer >= n occurs exactly once.

LINKS

Table of n, a(n) for n=1..78.

FORMULA

T(n,1) = n; T(n,2k) = 2T(n,k); T(n,2k+1) = 2T(n,k) + 1. T(n,k) = k + (n-1) * 2^floor(log_2(k)) = k + (n-1)*A053644(k).

EXAMPLE

Top left corner is:

1 2 3 4 5

2 4 5 8 9

3 6 7 12 13

4 8 9 16 17

5 10 11 20 21

CROSSREFS

Rows: A000027, A004754, A004755, A004756, A004757, A004758, A004759. Algebraically, A053645 would be row zero, minus A080079 would be row minus one. See also A053644.

Sequence in context: A106251 A134478 A051162 * A132919 A162619 A259196

Adjacent sequences:  A122869 A122870 A122871 * A122873 A122874 A122875

KEYWORD

easy,nonn,tabl

AUTHOR

Franklin T. Adams-Watters, Oct 23 2006

STATUS

approved

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Last modified October 17 18:58 EDT 2019. Contains 328127 sequences. (Running on oeis4.)