A261712 -id:A261712 - cp's OEIS frontend

A261727 Length of longest prefix of n-th row in A261712 coinciding with row n+1.

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

Offset: 1

Reinhard Zumkeller, Aug 31 2015

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

a261727 n = a261727_list !! (n-1)
a261727_list = map (length . takeWhile (== 0)) $
                   zipWith (zipWith (-)) a261712_tabf $ tail a261712_tabf

A261396 a(n) = smallest k such that A260273(k) >= 2^n.

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane, Aug 17 2015

nonn

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

Cf. A260273.

Cf. A261646, A261644, A261712.

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

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

A261644 Distance of A260273(n) to next power of 2.

Original entry on oeis.org

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

Offset: 1

Reinhard Zumkeller, Aug 30 2015

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

			.  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)

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

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

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)

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

A261646 Row lengths in A261644.

Original entry on oeis.org

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

Offset: 1

Reinhard Zumkeller, Aug 31 2015

nonn

First differences of A261396;

also row lengths in A261712.

Cf. A261644, A261712, A261396.

Haskell
```
a261646 = length . a261644_row
```

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

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

cp's OEIS Frontend

A261727 Length of longest prefix of n-th row in A261712 coinciding with row n+1.

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A261396 a(n) = smallest k such that A260273(k) >= 2^n.

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A261644 Distance of A260273(n) to next power of 2.

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A261646 Row lengths in A261644.

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