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.

A056963 Base 20 reversal of n (written in base 10).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1, 21, 41, 61, 81, 101, 121, 141, 161, 181, 201, 221, 241, 261, 281, 301, 321, 341, 361, 381, 2, 22, 42, 62, 82, 102, 122, 142, 162, 182, 202, 222, 242, 262, 282, 302, 322, 342, 362, 382, 3, 23, 43
Offset: 0

Views

Author

Henry Bottomley, Jul 18 2000

Keywords

Links

Crossrefs

Cf. A004086, A030101-A030108, A056960, A056961, A056962.

Programs

  • Mathematica
    IntegerReverse[Range[0, 100], 20] (* Paolo Xausa, Aug 08 2024 *)

A029730 Numbers that are palindromic in base 16.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 34, 51, 68, 85, 102, 119, 136, 153, 170, 187, 204, 221, 238, 255, 257, 273, 289, 305, 321, 337, 353, 369, 385, 401, 417, 433, 449, 465, 481, 497, 514, 530, 546, 562, 578, 594, 610, 626, 642
Offset: 1

Views

Author

Patrick De Geest

Keywords

Examples

			0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, 11, 22, 33, 44, 55, 66, 77, 88, 99, AA, BB, CC, DD, EE, FF, 101, 111, 121, 131, 141, 151, 161, 171, 181, 191,1A1, 1B1, 1C1, 1D1, 1E1, 1F1, 202, 212, 222, 232, 242, 252, 262, 272, 282, 292, 2A2, 2B2, 2C2, 2D2, 2E2, 2F2, 303, 313, 323, 333, 343, 353, 363, 373, 383, 393, 3A3, 3B3, 3C3, 3D3, 3E3, 3F3, 404, ... - _Reinhard Zumkeller_, Sep 23 2015

Links

Crossrefs

Cf. A029731 (also palindromic in decimal), A056962, A262437.

Programs

  • Haskell
    a029730 n = a029730_list !! (n-1)
a029730_list = map (foldr (\h v -> 16 * v + h) 0) $
                   filter (\xs -> xs == reverse xs) a262437_tabf
-- Reinhard Zumkeller, Sep 23 2015
  • Mathematica
    palindromicQ[n_, b_] := Module[{i = IntegerDigits[n, b]}, i == Reverse[i]]; Select[Range[1000], palindromicQ[#, 16] &] (* Vladimir Joseph Stephan Orlovsky, Jul 08 2009 *)
  • PARI
    isok(n) = my(v=digits(n,16)); v == Vecrev(v); \\ Michel Marcus, Sep 30 2018
  • Python
    def A029730(n):
    if n == 1: return 0
    y = (x:=1<<(n.bit_length()-2&-4))<<4
    return (c:=n-x)*x+int(hex(c)[-2:1:-1]or'0',16) if nChai Wah Wu, Jun 13 2024

Formula

Sum_{n>=2} 1/a(n) = 3.71109616... (Phunphayap and Pongsriiam, 2019). - Amiram Eldar, Oct 17 2020

A055964 n + reversal of hexadecimal (base 16) digits of n (written in base 10).

Original entry on oeis.org

0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 17, 34, 51, 68, 85, 102, 119, 136, 153, 170, 187, 204, 221, 238, 255, 272, 34, 51, 68, 85, 102, 119, 136, 153, 170, 187, 204, 221, 238, 255, 272, 289, 51, 68, 85, 102, 119, 136, 153, 170, 187, 204, 221, 238
Offset: 0

Views

Author

Henry Bottomley, Jul 18 2000

Keywords

Comments

If n has an even number of hexadecimal digits then a(n) is a multiple of 17.

Crossrefs

Cf. A056962, A056964.

Programs

  • Mathematica
    Table[n + IntegerReverse[n, 16], {n, 0, 100}] (* Paolo Xausa, Aug 08 2024 *)

Formula

a(n) = n + A056962(n).

A055965 n - reversal of hexadecimal (base 16) digits of n (written in base 10).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15, 0, -15, -30, -45, -60, -75, -90, -105, -120, -135, -150, -165, -180, -195, -210, 30, 15, 0, -15, -30, -45, -60, -75, -90, -105, -120, -135, -150, -165, -180, -195, 45, 30, 15, 0, -15, -30, -45, -60, -75, -90, -105, -120, -135, -150, -165, -180, 60, 45, 30, 15, 0
Offset: 0

Views

Author

Henry Bottomley, Jul 18 2000

Keywords

Comments

a(n) is a multiple of 15

Crossrefs

Cf. A056965.

Formula

a(n) =n-A056962(n)
Showing 1-4 of 4 results.

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