cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

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

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Author

N. J. A. Sloane, Aug 17 2015

Keywords

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

Crossrefs

Cf. A260273.
Cf. A261646, A261644, A261712.

Programs

  • 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

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

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

Views

Author

Reinhard Zumkeller, Aug 30 2015

Keywords

Comments

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

Examples

			.  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)

Links

Crossrefs

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

Programs

  • 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)

Formula

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

A261712 Reversed rows of A261644, seen as table read by rows.

Original entry on oeis.org

1, 1, 3, 1, 5, 8, 1, 5, 9, 12, 15, 3, 8, 13, 20, 25, 28, 31, 3, 8, 13, 17, 24, 29, 33, 37, 41, 44, 47, 52, 57, 60, 63, 2, 6, 10, 15, 24, 29, 33, 40, 47, 52, 57, 62, 66, 70, 77, 81, 85, 88, 91, 99, 105, 108, 111, 116, 121, 124, 127, 4, 12, 20, 25, 30, 34, 38
Offset: 1

Views

Author

Reinhard Zumkeller, Aug 31 2015

Keywords

Comments

T(n+1,k) = T(n,k) for k = 1 .. A261727(n).

Examples

			.   n |    T(n,*)                                            | A261646(n)
. ----+------------------------------------------------------+-----------
.   1 | 1                                                    |         1
.   2 | 1                                                    |         1
.   3 | 3                                                    |         1
.   4 | 1,5,8                                                |         3
.   5 | 1,5,9,12,15                                          |         5
.   6 | 3,8,13,20,25,28,31                                   |         7
.   7 | 3,8,13,17,24,29,33,37,41,44,47,52,57,60,63           |        15
.   8 | 2,6,10,15,24,29,33,40,47,52,57,62,66,70,77,81,85,... |        27
.   9 | 4,12,20,25,30,34,38,47,52,57,62,66,70,77,84,91,...   |        49
.  10 | 2,6,10,15,24,29,33,37,45,50,55,60,68,76,84,93,98,... |        90
.  11 | 2,6,10,15,24,29,33,37,45,50,55,60,68,76,84,93,98,... |       171
.  12 | 2,6,10,15,24,29,33,37,45,50,55,60,68,76,84,93,98,... |       326
.  13 | 2,6,10,15,24,29,33,37,45,50,55,60,68,76,84,93,98,... |       613
.  14 | 2,6,10,15,24,29,33,37,45,50,55,60,68,76,84,93,98,... |      1174
.  15 | 2,6,10,15,24,29,33,37,45,50,55,60,68,76,84,93,98,... |      2255
.  16 | 2,6,10,15,24,29,33,37,45,50,55,60,68,76,84,93,98,... |      4333 .

Links

Crossrefs

Cf. A261644, A261646 (row lengths), A261727.

Programs

  • Haskell
    a261712 n k = a261712_tabf !! (n-1) !! (k-1)
a261712_row n = a261712_tabf !! (n-1)
a261712_tabf = map reverse a261644_tabf

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

Original entry on oeis.org

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

Views

Author

Reinhard Zumkeller, Aug 31 2015

Keywords

Comments

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

Crossrefs

Cf. A261712, A261646, A261416.

Programs

  • Haskell
    a261727 n = a261727_list !! (n-1)
a261727_list = map (length . takeWhile (== 0)) $
                   zipWith (zipWith (-)) a261712_tabf $ tail a261712_tabf
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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