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 1-10 of 17 results. Next

A037013 Reading binary expansion from right to left, run lengths strictly decrease.

Original entry on oeis.org

0, 1, 3, 4, 7, 8, 15, 16, 24, 31, 32, 39, 48, 63, 64, 79, 96, 112, 127, 128, 143, 159, 192, 224, 255, 256, 287, 319, 384, 399, 448, 480, 511, 512, 543, 575, 624, 639, 768, 799, 896, 960, 1023, 1024, 1087, 1151, 1248, 1279, 1536, 1567, 1599, 1792, 1920, 1984, 2047, 2048, 2111
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Subsequence of A037014, cf. A037015, A037016.

Programs

  • Haskell
    import Data.List (unfoldr, group)
a037013 n = a037013_list !! (n-1)
a037013_list = 0 : filter
   (all (< 0) . (\x -> zipWith (-) (tail $ rls x) $ rls x)) [1..] where
       rls = map length . group . unfoldr
             (\x -> if x == 0 then Nothing else Just $ swap $ divMod x 2)
-- Reinhard Zumkeller, Mar 10 2012
  • Mathematica
    Select[Range[0,2200],Min[Differences[Length/@Split[ IntegerDigits[ #,2]]]]>0&] (* Harvey P. Dale, Dec 17 2012 *)

Extensions

More terms from Patrick De Geest, Feb 15 1999
Offset fixed and missing 1024 and 2047 inserted by Reinhard Zumkeller, Mar 10 2012

A037016 Numbers n with property that reading binary expansion from right to left (least significant to most significant), run lengths do not decrease.

Original entry on oeis.org

0, 1, 2, 3, 5, 6, 7, 10, 12, 13, 14, 15, 21, 25, 26, 28, 29, 30, 31, 42, 50, 51, 53, 56, 57, 58, 60, 61, 62, 63, 85, 101, 102, 106, 113, 114, 115, 117, 120, 121, 122, 124, 125, 126, 127, 170, 202, 204, 205, 213, 226, 227, 229, 230, 234, 240, 241, 242, 243, 245, 248
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

There are A000041(k) elements of this list consisting of k bits: a partition of k written in nonincreasing order corresponds to the binary expansion which when read left to right has run lengths as listed in the partition (reading left to right forces the initial run to be of 1s). - Jason Kimberley, Feb 08 2013
This sequence is a subsequence of A061854 (if we allow the initial 0 to be represented by the empty bit string). - Jason Kimberley, Feb 08 2013
The positive entries are those n for which row n of A101211 is weakly decreasing. Example: 6 is in the sequence because row 6 of A101211 is [2,1]; 8 is not in the sequence because row 8 of A101211 is [1,3]. - Emeric Deutsch, Jan 21 2018

Links

Crossrefs

Cf. A037015 (subsequence), A037014, A037013.

Programs

  • Haskell
    import Data.List (unfoldr, group)
a037016 n = a037016_list !! (n-1)
a037016_list = 0 : filter
   (all (>= 0) . (\x -> zipWith (-) (tail $ rls x) $ rls x)) [1..] where
       rls = map length . group . unfoldr
             (\x -> if x == 0 then Nothing else Just $ swap $ divMod x 2)
-- Reinhard Zumkeller, Mar 10 2012
  • Mathematica
    Select[ Range[0, 250], OrderedQ[ Reverse[ Length /@ Split[ IntegerDigits[#, 2] ] ] ]&] (* Jean-François Alcover, Apr 05 2013 *)

Extensions

More terms from Patrick De Geest, Feb 15 1999
Offset fixed by Reinhard Zumkeller, Mar 10 2012

A037014 Numbers n with property that reading binary expansion from right to left (from least significant to most significant), run lengths do not increase.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 7, 8, 10, 11, 12, 15, 16, 19, 20, 21, 23, 24, 31, 32, 39, 40, 42, 43, 44, 47, 48, 51, 56, 63, 64, 71, 76, 79, 80, 83, 84, 85, 87, 88, 95, 96, 103, 112, 127, 128, 143, 152, 159, 160, 167, 168, 170, 171, 172, 175, 176, 179, 184, 191, 192, 199, 204, 207
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A037013 (subsequence), A037016, A037015.

Programs

  • Haskell
    import Data.List (unfoldr, group)
a037014 n = a037014_list !! (n-1)
a037014_list = 0 : filter
   (all (<= 0) . (\x -> zipWith (-) (tail $ rls x) $ rls x)) [1..] where
       rls = map length . group . unfoldr
             (\x -> if x == 0 then Nothing else Just $ swap $ divMod x 2)
-- Reinhard Zumkeller, Mar 10 2012
  • Mathematica
    Select[Range[0,250],Min[Differences[Length/@Split[IntegerDigits[ #,2]]]]>= 0&] (* Harvey P. Dale, Jan 30 2013 *)

Extensions

More terms from Patrick De Geest, Feb 15 1999
Offset fixed by Reinhard Zumkeller, Mar 10 2012

A048300 Numbers whose base-3 expansions, read from left to right, have run lengths that strictly increase.

Original entry on oeis.org

0, 1, 2, 4, 8, 9, 13, 17, 18, 22, 26, 27, 40, 53, 54, 67, 80, 81, 108, 121, 134, 161, 162, 202, 216, 229, 242, 243, 256, 269, 324, 364, 404, 459, 472, 485, 486, 499, 512, 594, 607, 620, 648, 688, 728, 729, 769, 809, 972, 1053, 1093, 1133, 1214, 1377, 1417
Offset: 0

Views

Author

Patrick De Geest, Feb 15 1999

Keywords

Crossrefs

Cf. A037015, A043692, A043706, A044814, A044952.

A048301 Numbers whose base-4 expansions, read from left to right, have run lengths that strictly increase.

Original entry on oeis.org

0, 1, 2, 3, 5, 10, 15, 16, 21, 26, 31, 32, 37, 42, 47, 48, 53, 58, 63, 64, 85, 106, 127, 128, 149, 170, 191, 192, 213, 234, 255, 256, 320, 341, 362, 383, 426, 511, 512, 597, 640, 661, 682, 703, 767, 768, 853, 938, 960, 981, 1002, 1023, 1024, 1045, 1066, 1087
Offset: 0

Views

Author

Patrick De Geest, Feb 15 1999

Keywords

Crossrefs

Cf. A037015, A043693, A043707, A044815, A044953.

A048302 Numbers whose base-5 expansions, read from left to right, have run lengths that strictly increase.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 12, 18, 24, 25, 31, 37, 43, 49, 50, 56, 62, 68, 74, 75, 81, 87, 93, 99, 100, 106, 112, 118, 124, 125, 156, 187, 218, 249, 250, 281, 312, 343, 374, 375, 406, 437, 468, 499, 500, 531, 562, 593, 624, 625, 750, 781, 812, 843, 874, 937, 1093, 1249
Offset: 0

Views

Author

Patrick De Geest, Feb 15 1999

Keywords

Crossrefs

Cf. A037015, A043694, A043708, A044816, A044954.

A048303 Numbers whose base-6 expansions, read from left to right, have run lengths that strictly increase.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 7, 14, 21, 28, 35, 36, 43, 50, 57, 64, 71, 72, 79, 86, 93, 100, 107, 108, 115, 122, 129, 136, 143, 144, 151, 158, 165, 172, 179, 180, 187, 194, 201, 208, 215, 216, 259, 302, 345, 388, 431, 432, 475, 518, 561, 604, 647, 648, 691, 734, 777, 820
Offset: 0

Views

Author

Patrick De Geest, Feb 15 1999

Keywords

Crossrefs

Cf. A037015, A043695, A043709, A044817, A044955.

Programs

  • Mathematica
    Select[Range[0,900],Min[Differences[Length/@Split[IntegerDigits[ #,6]]]]> 0&] (* Harvey P. Dale, Jan 14 2014 *)

A048304 Numbers whose base-7 expansions, read from left to right, have run lengths that strictly increase.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 8, 16, 24, 32, 40, 48, 49, 57, 65, 73, 81, 89, 97, 98, 106, 114, 122, 130, 138, 146, 147, 155, 163, 171, 179, 187, 195, 196, 204, 212, 220, 228, 236, 244, 245, 253, 261, 269, 277, 285, 293, 294, 302, 310, 318, 326, 334, 342, 343, 400, 457
Offset: 0

Views

Author

Patrick De Geest, Feb 15 1999

Keywords

Crossrefs

Cf. A037015, A043696, A043710, A044818, A044956.

A048305 Numbers whose base-8 expansions, read from left to right, have run lengths that strictly increase.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 9, 18, 27, 36, 45, 54, 63, 64, 73, 82, 91, 100, 109, 118, 127, 128, 137, 146, 155, 164, 173, 182, 191, 192, 201, 210, 219, 228, 237, 246, 255, 256, 265, 274, 283, 292, 301, 310, 319, 320, 329, 338, 347, 356, 365, 374, 383, 384, 393, 402
Offset: 0

Views

Author

Patrick De Geest, Feb 15 1999

Keywords

Crossrefs

Cf. A037015, A043697, A043711, A044819, A044957.

Programs

  • Mathematica
    Select[Range[0,500],Min[Differences[Length/@Split[IntegerDigits[ #,8]]]]>0&] (* Harvey P. Dale, Dec 06 2018 *)

A048306 Numbers whose base-9 expansions, read from left to right, have run lengths that strictly increase.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 20, 30, 40, 50, 60, 70, 80, 81, 91, 101, 111, 121, 131, 141, 151, 161, 162, 172, 182, 192, 202, 212, 222, 232, 242, 243, 253, 263, 273, 283, 293, 303, 313, 323, 324, 334, 344, 354, 364, 374, 384, 394, 404, 405, 415, 425, 435, 445
Offset: 0

Views

Author

Patrick De Geest, Feb 15 1999

Keywords

Crossrefs

Cf. A037015, A043698, A043712, A044820, A044958.
Showing 1-10 of 17 results. Next

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

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