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.

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A055117 Base-7 complement of n (write n in base 7, then replace each digit with its base-7 negative).

Original entry on oeis.org

0, 6, 5, 4, 3, 2, 1, 42, 48, 47, 46, 45, 44, 43, 35, 41, 40, 39, 38, 37, 36, 28, 34, 33, 32, 31, 30, 29, 21, 27, 26, 25, 24, 23, 22, 14, 20, 19, 18, 17, 16, 15, 7, 13, 12, 11, 10, 9, 8, 294, 300, 299, 298, 297, 296, 295, 336, 342, 341, 340, 339, 338, 337, 329, 335, 334
Offset: 0

Views

Author

Henry Bottomley, Apr 19 2000

Keywords

Links

Crossrefs

Cf. A004488, A048647, A055115-A055126.
Column k=7 of A248813.

A055118 Base-8 complement of n (write n in base 8, then replace each digit with its base-8 negative).

Original entry on oeis.org

0, 7, 6, 5, 4, 3, 2, 1, 56, 63, 62, 61, 60, 59, 58, 57, 48, 55, 54, 53, 52, 51, 50, 49, 40, 47, 46, 45, 44, 43, 42, 41, 32, 39, 38, 37, 36, 35, 34, 33, 24, 31, 30, 29, 28, 27, 26, 25, 16, 23, 22, 21, 20, 19, 18, 17, 8, 15, 14, 13, 12, 11, 10, 9, 448, 455, 454, 453, 452, 451
Offset: 0

Views

Author

Henry Bottomley, Apr 19 2000

Keywords

Links

Crossrefs

Cf. A004488, A048647, A055115-A055126.
Column k=8 of A248813.

Programs

  • Haskell
    a055118 0 = 0
a055118 n = if d == 0 then 8 * a055118 n' else 8 * a055118 n' + 8 - d
            where (n', d) = divMod n 8
-- Reinhard Zumkeller, Mar 12 2014

A055119 Base-9 complement of n (write n in base 9, then replace each digit with its base-9 negative).

Original entry on oeis.org

0, 8, 7, 6, 5, 4, 3, 2, 1, 72, 80, 79, 78, 77, 76, 75, 74, 73, 63, 71, 70, 69, 68, 67, 66, 65, 64, 54, 62, 61, 60, 59, 58, 57, 56, 55, 45, 53, 52, 51, 50, 49, 48, 47, 46, 36, 44, 43, 42, 41, 40, 39, 38, 37, 27, 35, 34, 33, 32, 31, 30, 29, 28, 18, 26, 25, 24, 23, 22, 21, 20, 19
Offset: 0

Views

Author

Henry Bottomley, Apr 19 2000

Keywords

Links

Crossrefs

Cf. A004488, A048647, A055115-A055126.
Column k=9 of A248813.

A055121 Base-11 complement of n (write n in base 11, then replace each digit with its base-11 negative).

Original entry on oeis.org

0, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 110, 120, 119, 118, 117, 116, 115, 114, 113, 112, 111, 99, 109, 108, 107, 106, 105, 104, 103, 102, 101, 100, 88, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 77, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 66, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67
Offset: 0

Views

Author

Henry Bottomley, Apr 19 2000

Keywords

Links

Crossrefs

Cf. A004488, A048647, A055115-A055126.
Column k=11 of A248813.

A055122 Base-12 complement of n (write n in base 12, then replace each digit with its base-12 negative).

Original entry on oeis.org

0, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 132, 143, 142, 141, 140, 139, 138, 137, 136, 135, 134, 133, 120, 131, 130, 129, 128, 127, 126, 125, 124, 123, 122, 121, 108, 119, 118, 117, 116, 115, 114, 113, 112, 111, 110, 109, 96, 107, 106, 105, 104, 103, 102, 101, 100, 99
Offset: 0

Views

Author

Henry Bottomley, Apr 19 2000

Keywords

Links

Crossrefs

Cf. A004488, A048647, A055115-A055126.
Column k=12 of A248813.

Programs

  • Haskell
    a055122 0 = 0
a055122 n = if d == 0 then 12 * a055122 n' else 12 * a055122 n' + 12 - d
            where (n', d) = divMod n 12
-- Reinhard Zumkeller, Mar 12 2014

A055123 Base-13 complement of n (write n in base 13, then replace each digit with its base-13 negative).

Original entry on oeis.org

0, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 156, 168, 167, 166, 165, 164, 163, 162, 161, 160, 159, 158, 157, 143, 155, 154, 153, 152, 151, 150, 149, 148, 147, 146, 145, 144, 130, 142, 141, 140, 139, 138, 137, 136, 135, 134, 133, 132, 131, 117, 129, 128, 127, 126
Offset: 0

Views

Author

Henry Bottomley, Apr 19 2000

Keywords

Links

Crossrefs

Cf. A004488, A048647, A055115-A055126.
Column k=13 of A248813.

A055124 Base-14 complement of n (write n in base 14, then replace each digit with its base-14 negative).

Original entry on oeis.org

0, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 182, 195, 194, 193, 192, 191, 190, 189, 188, 187, 186, 185, 184, 183, 168, 181, 180, 179, 178, 177, 176, 175, 174, 173, 172, 171, 170, 169, 154, 167, 166, 165, 164, 163, 162, 161, 160, 159, 158, 157, 156, 155, 140
Offset: 0

Views

Author

Henry Bottomley, Apr 19 2000

Keywords

Links

Crossrefs

Cf. A004488, A048647, A055115-A055126.
Column k=14 of A248813.

Programs

  • Haskell
    a055124 0 = 0
a055124 n = if d == 0 then 14 * a055124 n' else 14 * a055124 n' + 14 - d
            where (n', d) = divMod n 14
-- Reinhard Zumkeller, Mar 12 2014

A055125 Base-15 complement of n (write n in base 15, then replace each digit with its base-15 negative).

Original entry on oeis.org

0, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 210, 224, 223, 222, 221, 220, 219, 218, 217, 216, 215, 214, 213, 212, 211, 195, 209, 208, 207, 206, 205, 204, 203, 202, 201, 200, 199, 198, 197, 196, 180, 194, 193, 192, 191, 190, 189, 188, 187, 186, 185, 184
Offset: 0

Views

Author

Henry Bottomley, Apr 19 2000

Keywords

Links

Crossrefs

Cf. A004488, A048647, A055115-A055126.
Column k=15 of A248813.

A318724 Let f(0) = 0 and f(t*4^k + u) = i^t * ((1+i) * 2^k - f(u)) for any t in {1, 2, 3} and k >= 0 and u such that 0 <= u < 4^k (i denoting the imaginary unit); for any n >= 0, let g(n) = (f(A042968(n)) - 1 - i) / 2; a(n) is the square of the modulus of g(n).

Original entry on oeis.org

1, 2, 1, 2, 5, 4, 5, 8, 5, 4, 5, 2, 8, 13, 10, 5, 10, 13, 18, 25, 20, 17, 16, 9, 13, 18, 13, 10, 17, 20, 25, 32, 25, 20, 17, 10, 10, 13, 8, 9, 16, 17, 20, 25, 18, 13, 10, 5, 32, 41, 34, 25, 34, 41, 50, 61, 52, 45, 40, 29, 29, 40, 45, 20, 17, 26, 37, 50, 53, 58
Offset: 0

Views

Author

Rémy Sigrist, Sep 02 2018

Keywords

Comments

See A318722 for the real part of g and additional comments.

Links

Crossrefs

Cf. A042968, A048647, A318722, A318723.

Programs

  • PARI
    a(n) = my (d=Vecrev(digits(1+n+n\3,4)), z=0); for (k=1, #d, if (d[k], z = I^d[k] * (-z + (1+I) * 2^(k-1)))); norm((z-1-I)/2)

Formula

a(n) = A318722(n)^2 + A318723(n)^2.
If A048647(A042968(m)) = A042968(n), then a(m) = a(n).

A348354 The base-5 expansion of a(n) is obtained by replacing 1's, 2's, 3's and 4's by 3's, 4's, 1's and 2's, respectively, in the base-5 expansion of n.

Original entry on oeis.org

0, 3, 4, 1, 2, 15, 18, 19, 16, 17, 20, 23, 24, 21, 22, 5, 8, 9, 6, 7, 10, 13, 14, 11, 12, 75, 78, 79, 76, 77, 90, 93, 94, 91, 92, 95, 98, 99, 96, 97, 80, 83, 84, 81, 82, 85, 88, 89, 86, 87, 100, 103, 104, 101, 102, 115, 118, 119, 116, 117, 120, 123, 124, 121
Offset: 0

Views

Author

Rémy Sigrist, Oct 14 2021

Keywords

Comments

This sequence is a self-inverse permutation of the nonnegative integers.
It is possible to build a similar sequence for any fixed base b > 1 and any permutation p of {1, ..., b-1}.
This sequence is interesting as it satisfies f(a(n)) = -f(n), where f(n) = (A316657(n), A316658(n)).

Examples

			The first terms, in decimal and in base 5, are:
  n   a(n)  q(n)  q(a(n))
  --  ----  ----  -------
   0     0     0        0
   1     3     1        3
   2     4     2        4
   3     1     3        1
   4     2     4        2
   5    15    10       30
   6    18    11       33
   7    19    12       34
   8    16    13       31
   9    17    14       32
  10    20    20       40

Links

Crossrefs

See A004488, A048647 and A348355 for similar sequences.
Cf. A316657, A316658.

Programs

  • Mathematica
    a[n_] := With[{d = {0, 3, 4, 1, 2}}, FromDigits[d[[IntegerDigits[n, 5] + 1]], 5]]; Array[a, 64, 0] (* Amiram Eldar, Oct 16 2021 *)
  • PARI
    a(n, p=[3,4,1,2]) = fromdigits(apply(d -> if (d, p[d], 0), digits(n, #p+1)), #p+1)

Formula

A316657(n) + A316657(a(n)) = 0.
A316658(n) + A316658(a(n)) = 0.
Previous Showing 11-20 of 23 results. Next

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