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 16 results. Next

A160700 a(n) = if n<16 then n else a(floor(n/16)) XOR (n mod 16).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 1, 0, 3, 2, 5, 4, 7, 6, 9, 8, 11, 10, 13, 12, 15, 14, 2, 3, 0, 1, 6, 7, 4, 5, 10, 11, 8, 9, 14, 15, 12, 13, 3, 2, 1, 0, 7, 6, 5, 4, 11, 10, 9, 8, 15, 14, 13, 12, 4, 5, 6, 7, 0, 1, 2, 3, 12, 13, 14, 15, 8, 9, 10, 11, 5, 4, 7, 6, 1, 0, 3, 2, 13
Offset: 0

Views

Author

Reinhard Zumkeller, Jun 01 2009

Keywords

Comments

A very simple hash function for the nonnegative integers.
a(A000079(n))=A133145(n); a(A000302(n))=A010685(n); a(A001025(n))=A161452(n); a(A161440(n))=0; a(A161441(n))=1; a(A161442(n))=2; a(A161443(n))=3; a(A161444(n))=4; a(A161445(n))=5; a(A161446(n))=6; a(A161447(n))=7; a(A161448(n))=8; a(A161449(n))=9; a(A161450(n))=10; a(A161451(n))=11; a(A161452(n))=12; a(A161453(n))=13; a(A161454(n))=14; a(A161455(n))=15. - Reinhard Zumkeller, Jun 10 2009

Links

Programs

  • Haskell
    import Data.Bits (xor)
a160700 n = a160700_list !! n
a160700_list = [0..15] ++ map f [16..] where
   f x = a160700 x' `xor` m :: Int where (x', m) = divMod x 16
-- Reinhard Zumkeller, Nov 07 2012
  • Maple
    read("transforms") ;
A160700 := proc(n)
    if n < 16 then
        n;
    else
        XORnos(procname(floor(n/16)),modp(n,16))
    end if;
end proc: # R. J. Mathar, Jul 12 2016
  • Mathematica
    a[n_] := a[n] = If[n < 16, n, a[Floor[n/16]] ~BitXor~ Mod[n, 16]];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Jan 25 2018 *)
  • Maxima
    load(functs)$
A160700(n):=if n<16 then n else logxor(floor(n/16),mod(n,16))$
makelist(A160700(n),n,0,60); /* Martin Ettl, Nov 05 2012 */
  • PARI
    a(n)=my(t=n%16); while(n>15, n>>=4; t=bitxor(t, n%16)); t \\ Charles R Greathouse IV, Jan 25 2018

A161441 Numbers n such that A160700(n) = 1.

Original entry on oeis.org

1, 16, 35, 50, 69, 84, 103, 118, 137, 152, 171, 186, 205, 220, 239, 254, 256, 273, 290, 307, 324, 341, 358, 375, 392, 409, 426, 443, 460, 477, 494, 511, 515, 530, 545, 560, 583, 598, 613, 628, 651, 666, 681, 696, 719, 734, 749, 764, 770, 787, 800, 817, 838
Offset: 1

Views

Author

Reinhard Zumkeller, Jun 10 2009

Keywords

Links

Crossrefs

A001025 is a subsequence.
Cf. A161440, A161442, A161443, A161444, A161445, A161446, A161447, A161448, A161449, A161450, A161451, A161452, A161453, A161454, A161455.

Programs

  • Mathematica
    b[n_] := b[n] = If[n < 16, n, b[Floor[n/16]]~BitXor~Mod[n, 16]];
Select[Range[0, 1000], b[#] == 1&] (* Jean-François Alcover, Dec 01 2021 *)
  • PARI
    A160700(n)=my(t=n%16); while(n>15, n>>=4; t=bitxor(t, n%16)); t
a(n)=for(k=16*n-16,16*n-1, if(a(k)==1, return(k))) \\ Charles R Greathouse IV, Jan 25 2018

Formula

16n - 16 <= a(n) <= 16n - 1. - Charles R Greathouse IV, Jan 25 2018

A161447 Numbers n such that A160700(n) = 7.

Original entry on oeis.org

7, 22, 37, 52, 67, 82, 97, 112, 143, 158, 173, 188, 203, 218, 233, 248, 262, 279, 292, 309, 322, 339, 352, 369, 398, 415, 428, 445, 458, 475, 488, 505, 517, 532, 551, 566, 577, 592, 611, 626, 653, 668, 687, 702, 713, 728, 747, 762, 772, 789, 806, 823, 832
Offset: 1

Views

Author

Reinhard Zumkeller, Jun 10 2009

Keywords

Links

Crossrefs

Cf. A161440, A161441, A161442, A161443, A161444, A161445, A161446, A161448, A161449, A161450, A161451, A161452, A161453, A161454, A161455.

Programs

  • PARI
    A160700(n)=my(t=n%16); while(n>15, n>>=4; t=bitxor(t, n%16)); t
a(n)=for(k=16*n-16, 16*n-1, if(a(k)==7, return(k))) \\ Charles R Greathouse IV, Jan 25 2018

Formula

16n - 16 <= a(n) <= 16n - 1. - Charles R Greathouse IV, Jan 25 2018

A161440 Numbers m such that A160700(m) = 0.

Original entry on oeis.org

0, 17, 34, 51, 68, 85, 102, 119, 136, 153, 170, 187, 204, 221, 238, 255, 257, 272, 291, 306, 325, 340, 359, 374, 393, 408, 427, 442, 461, 476, 495, 510, 514, 531, 544, 561, 582, 599, 612, 629, 650, 667, 680, 697, 718, 735, 748, 765, 771, 786, 801, 816, 839
Offset: 1

Views

Author

Reinhard Zumkeller, Jun 10 2009

Keywords

Links

Crossrefs

Cf. A160700.
Cf. A161441, A161442, A161443, A161444, A161445, A161446, A161447, A161448, A161449, A161450, A161451, A161452, A161453, A161454, A161455.

Programs

  • Mathematica
    b[n_] := b[n] = If[n < 16, n, b[Floor[n/16]]~BitXor~Mod[n, 16]];
Select[Range[0, 1000], b[#] == 0&] (* Jean-François Alcover, Dec 01 2021 *)
  • PARI
    A160700(n)=my(t=n%16); while(n>15, n>>=4; t=bitxor(t, n%16)); t
a(n)=for(k=16*n-16,16*n-1, if(a(k)==0, return(k))) \\ Charles R Greathouse IV, Jan 25 2018

Formula

16n - 16 <= a(n) <= 16n - 1. - Charles R Greathouse IV, Jan 25 2018

A161442 Numbers n such that A160700(n) = 2.

Original entry on oeis.org

2, 19, 32, 49, 70, 87, 100, 117, 138, 155, 168, 185, 206, 223, 236, 253, 259, 274, 289, 304, 327, 342, 357, 372, 395, 410, 425, 440, 463, 478, 493, 508, 512, 529, 546, 563, 580, 597, 614, 631, 648, 665, 682, 699, 716, 733, 750, 767, 769, 784, 803, 818, 837
Offset: 1

Views

Author

Reinhard Zumkeller, Jun 10 2009

Keywords

Links

Crossrefs

Cf. A161440, A161441, A161443, A161444, A161445, A161446, A161447, A161448, A161449, A161450, A161451, A161452, A161453, A161454, A161455.

Programs

  • PARI
    A160700(n)=my(t=n%16); while(n>15, n>>=4; t=bitxor(t, n%16)); t
a(n)=for(k=16*n-16,16*n-1, if(a(k)==2, return(k))) \\ Charles R Greathouse IV, Jan 25 2018

Formula

16n - 16 <= a(n) <= 16n - 1. - Charles R Greathouse IV, Jan 25 2018

A161443 Numbers m such that A160700(m) = 3.

Original entry on oeis.org

3, 18, 33, 48, 71, 86, 101, 116, 139, 154, 169, 184, 207, 222, 237, 252, 258, 275, 288, 305, 326, 343, 356, 373, 394, 411, 424, 441, 462, 479, 492, 509, 513, 528, 547, 562, 581, 596, 615, 630, 649, 664, 683, 698, 717, 732, 751, 766, 768, 785, 802, 819, 836
Offset: 1

Views

Author

Reinhard Zumkeller, Jun 10 2009

Keywords

Links

Crossrefs

Cf. A161440, A161441, A161442, A161444, A161445, A161446, A161447, A161448, A161449, A161450, A161451, A161452, A161453, A161454, A161455.

Programs

  • PARI
    A160700(n)=my(t=n%16); while(n>15, n>>=4; t=bitxor(t, n%16)); t
a(n)=for(k=16*n-16, 16*n-1, if(a(k)==3, return(k))) \\ Charles R Greathouse IV, Jan 25 2018

Formula

16n - 16 <= a(n) <= 16n - 1. - Charles R Greathouse IV, Jan 25 2018

A161444 Numbers n such that A160700(n) = 4.

Original entry on oeis.org

4, 21, 38, 55, 64, 81, 98, 115, 140, 157, 174, 191, 200, 217, 234, 251, 261, 276, 295, 310, 321, 336, 355, 370, 397, 412, 431, 446, 457, 472, 491, 506, 518, 535, 548, 565, 578, 595, 608, 625, 654, 671, 684, 701, 714, 731, 744, 761, 775, 790, 805, 820, 835
Offset: 1

Views

Author

Reinhard Zumkeller, Jun 10 2009

Keywords

Links

Crossrefs

A161440, A161441, A161442, A161443, A161445, A161446, A161447, A161448, A161449, A161450, A161451, A161452, A161453, A161454, A161455.

Programs

  • PARI
    A160700(n)=my(t=n%16); while(n>15, n>>=4; t=bitxor(t, n%16)); t
a(n)=for(k=16*n-16, 16*n-1, if(a(k)==4, return(k))) \\ Charles R Greathouse IV, Jan 25 2018

Formula

16n - 16 <= a(n) <= 16n - 1. - Charles R Greathouse IV, Jan 25 2018

A161445 Numbers n such that A160700(n) = 5.

Original entry on oeis.org

5, 20, 39, 54, 65, 80, 99, 114, 141, 156, 175, 190, 201, 216, 235, 250, 260, 277, 294, 311, 320, 337, 354, 371, 396, 413, 430, 447, 456, 473, 490, 507, 519, 534, 549, 564, 579, 594, 609, 624, 655, 670, 685, 700, 715, 730, 745, 760, 774, 791, 804, 821, 834
Offset: 1

Views

Author

Reinhard Zumkeller, Jun 10 2009

Keywords

Links

Crossrefs

Cf. A161440, A161441, A161442, A161443, A161444, A161446, A161447, A161448, A161449, A161450, A161451, A161452, A161453, A161454, A161455.

Programs

  • PARI
    A160700(n)=my(t=n%16); while(n>15, n>>=4; t=bitxor(t, n%16)); t
a(n)=for(k=16*n-16, 16*n-1, if(a(k)==5, return(k))) \\ Charles R Greathouse IV, Jan 25 2018

Formula

16n - 16 <= a(n) <= 16n - 1. - Charles R Greathouse IV, Jan 25 2018

A161446 Numbers n such that A160700(n) = 6.

Original entry on oeis.org

6, 23, 36, 53, 66, 83, 96, 113, 142, 159, 172, 189, 202, 219, 232, 249, 263, 278, 293, 308, 323, 338, 353, 368, 399, 414, 429, 444, 459, 474, 489, 504, 516, 533, 550, 567, 576, 593, 610, 627, 652, 669, 686, 703, 712, 729, 746, 763, 773, 788, 807, 822, 833
Offset: 1

Views

Author

Reinhard Zumkeller, Jun 10 2009

Keywords

Links

Crossrefs

Cf. A161440, A161441, A161442, A161443, A161444, A161445, A161447, A161448, A161449, A161450, A161451, A161452, A161453, A161454, A161455.

Programs

  • PARI
    A160700(n)=my(t=n%16); while(n>15, n>>=4; t=bitxor(t, n%16)); t
a(n)=for(k=16*n-16, 16*n-1, if(a(k)==6, return(k))) \\ Charles R Greathouse IV, Jan 25 2018

Formula

16n - 16 <= a(n) <= 16n - 1. - Charles R Greathouse IV, Jan 25 2018

A161448 Numbers n such that A160700(n) = 8.

Original entry on oeis.org

8, 25, 42, 59, 76, 93, 110, 127, 128, 145, 162, 179, 196, 213, 230, 247, 265, 280, 299, 314, 333, 348, 367, 382, 385, 400, 419, 434, 453, 468, 487, 502, 522, 539, 552, 569, 590, 607, 620, 637, 642, 659, 672, 689, 710, 727, 740, 757, 779, 794, 809, 824, 847
Offset: 1

Views

Author

Reinhard Zumkeller, Jun 10 2009

Keywords

Links

Crossrefs

Cf. A161440, A161441, A161442, A161443, A161444, A161445, A161446, A161447, A161449, A161450, A161451, A161452, A161453, A161454, A161455.

Programs

  • PARI
    A160700(n)=my(t=n%16); while(n>15, n>>=4; t=bitxor(t, n%16)); t
a(n)=for(k=16*n-16, 16*n-1, if(a(k)==8, return(k))) \\ Charles R Greathouse IV, Jan 25 2018

Formula

16n - 16 <= a(n) <= 16n - 1. - Charles R Greathouse IV, Jan 25 2018
Showing 1-10 of 16 results. Next

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