A261712 -id:A261712

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A261727

Length of longest prefix of n-th row in A261712 coinciding with row n+1.

+20
2

1, 0, 0, 2, 0, 3, 0, 0, 0, 25, 46, 90, 172, 141, 275, 601, 1102, 2199, 4150

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,4

COMMENTS

A261712(n+1,k) = A261712(n,k) for k = 1 .. a(n).

LINKS

Table of n, a(n) for n=1..19.

PROG

(Haskell)

a261727 n = a261727_list !! (n-1)

a261727_list = map (length . takeWhile (== 0)) $

zipWith (zipWith (-)) a261712_tabf $ tail a261712_tabf

CROSSREFS

Cf. A261712, A261646, A261416.

KEYWORD

nonn,more

AUTHOR

Reinhard Zumkeller, Aug 31 2015

STATUS

approved

A261396

a(n) = smallest k such that A260273(k) >= 2^n.

+10
6

1, 2, 3, 4, 7, 12, 19, 34, 61, 110, 200, 371, 697, 1310, 2484, 4739, 9072, 17458, 33671, 65128, 126225, 244802, 475124, 922891, 1793461, 3487348, 6784691, 13208038, 25731600, 50166771, 97873783, 191089176, 373349780, 729972649, 1428257200, 2796453078, 5478981032, 10741710906, 21072415837

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

The sequence indicates the first time a term in A260273 has binary length n+1.

A261646 = first differences = row lengths of tables A261644 and A261712. - Reinhard Zumkeller, Aug 30 2015

LINKS

Table of n, a(n) for n=0..38.

PROG

(Haskell)

a261396 n = a261396_list !! (n-1)

a261396_list = f 1 1 a260273_list where

f z k (x:xs) | x >= z = k : f (2 * z) (k + 1) xs

| otherwise = f z (k + 1) xs

-- Reinhard Zumkeller, Aug 30 2015

CROSSREFS

Cf. A260273.

Cf. A261646, A261644, A261712.

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Aug 17 2015

EXTENSIONS

a(18)-a(23) from Alois P. Heinz, Aug 19 2015

a(24)-a(34) from Chai Wah Wu, Aug 26 2015

a(35)-a(38) from Chai Wah Wu, Aug 31 2015

STATUS

approved

A261644

Distance of A260273(n) to next power of 2.

+10
6

1, 1, 3, 8, 5, 1, 15, 12, 9, 5, 1, 31, 28, 25, 20, 13, 8, 3, 63, 60, 57, 52, 47, 44, 41, 37, 33, 29, 24, 17, 13, 8, 3, 127, 124, 121, 116, 111, 108, 105, 99, 91, 88, 85, 81, 77, 70, 66, 62, 57, 52, 47, 40, 33, 29, 24, 15, 10, 6, 2, 254, 251, 248, 245, 239

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

COMMENTS

This sequence, as well as A261712, is suggested by A261396 and A261416.

LINKS

Reinhard Zumkeller, Rows n = 1..20 of triangle, flattened

FORMULA

a(n) = A062383(A260273(n)) - A260273(n).

EXAMPLE

. 1: 1

. 2: 1

. 3: 3

. 4: 8,5,1

. 5: 15,12,9,5,1

. 6: 31,28,25,20,13,8,3

. 7: 63,60,57,52,47,44,41,37,33,29,24,17,13,8,3

. 8: 127,124,121,116,111,108,105,99,91,88,85,81,77,70,... (27 terms)

. 9: 254,251,248,245,239,236,233,227,218,213,207,202,195,,... (49 terms)

PROG

(Haskell)

a261644 n = a261644_list !! (n-1)

a261644_list = zipWith (-)

(map a062383 a260273_list) $ map fromIntegral a260273_list

a261644_tabf = [1] : f (tail $ zip a261645_list a261644_list) where

f dxs = (map snd (dxs'' ++ [dx])) : f dxs' where

(dxs'', dx:dxs') = span ((<= 0) . fst) dxs

a261644_row n = a261644_tabf !! (n-1)

CROSSREFS

Cf. A260273, A062383, A261645 (first differences), A261712 (reversed), A261646 (row lengths).

KEYWORD

nonn,tabf

AUTHOR

Reinhard Zumkeller, Aug 30 2015

STATUS

approved

A261646

Row lengths in A261644.

+10
5

1, 1, 1, 3, 5, 7, 15, 27, 49, 90, 171, 326, 613, 1174, 2255, 4333, 8386, 16213, 31457, 61097, 118577, 230322, 447767, 870570, 1693887, 3297343, 6423347, 12523562, 24435171, 47707012, 93215393, 182260604, 356622869, 698284551, 1368195878, 2682527954, 5262729874, 10330704931

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,4

COMMENTS

First differences of A261396;

also row lengths in A261712.

LINKS

Table of n, a(n) for n=1..38.

FORMULA

a(n) = A261396(n) - A261396(n-1).

PROG

(Haskell)

a261646 = length . a261644_row

CROSSREFS

Cf. A261644, A261712, A261396.

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Aug 31 2015

EXTENSIONS

a(21)-a(38) from Chai Wah Wu, Aug 31 2015

STATUS

approved

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