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 11 results. Next

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 *)

A056961 Base 12 reversal of n (written in base 10).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 1, 13, 25, 37, 49, 61, 73, 85, 97, 109, 121, 133, 2, 14, 26, 38, 50, 62, 74, 86, 98, 110, 122, 134, 3, 15, 27, 39, 51, 63, 75, 87, 99, 111, 123, 135, 4, 16, 28, 40, 52, 64, 76, 88, 100, 112, 124, 136, 5, 17, 29, 41, 53, 65, 77, 89, 101
Offset: 0

Views

Author

Henry Bottomley, Jul 18 2000

Keywords

Links

Crossrefs

Cf. A004086, A030101-A030108, A056960-A056963.

Programs

  • Mathematica
    IntegerReverse[Range[0, 100], 12] (* Paolo Xausa, Aug 08 2024 *)

A056962 Base 16 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, 1, 17, 33, 49, 65, 81, 97, 113, 129, 145, 161, 177, 193, 209, 225, 241, 2, 18, 34, 50, 66, 82, 98, 114, 130, 146, 162, 178, 194, 210, 226, 242, 3, 19, 35, 51, 67, 83, 99, 115, 131, 147, 163, 179, 195, 211, 227, 243, 4
Offset: 0

Views

Author

Henry Bottomley, Jul 18 2000

Keywords

Examples

			a(17) = 17 because 17 in hexadecimal is 11, the same as its reverse.
a(18) = 33 because 18 in hexadecimal is 12, and hexadecimal 21 is 2 * 16 + 1 = 33.
a(19) = 49 because 19 in hexadecimal is 13, and hexadecimal 31 is 3 * 16 + 1 = 49.

Crossrefs

Cf. A004086, A030101-A030108, A056960-A056963, A029730.

Programs

  • Mathematica
    Table[FromDigits[Reverse[IntegerDigits[n, 16]], 16], {n, 0, 127}] (* Alonso del Arte, Sep 30 2018 *)
  • PARI
    a(n) = fromdigits(Vecrev(digits(n, 16)), 16); \\ Michel Marcus, Sep 30 2018

A091974 Let R_{k}(n) = the digit reversal of n in base k (R_{k}(n) is written in base 10). a(n) is the number of distinct values of R_{k}(n) arising if k=2,..,n+1.

Original entry on oeis.org

1, 1, 2, 2, 2, 3, 5, 5, 5, 6, 7, 9, 9, 11, 11, 12, 11, 14, 13, 16, 16, 17, 19, 21, 19, 22, 22, 21, 23, 24, 27, 27, 27, 29, 29, 32, 29, 35, 33, 36, 32, 38, 37, 41, 39, 41, 40, 42, 41, 45, 43, 45, 46, 48, 47, 49, 50, 52, 52, 55, 53, 57, 58, 56, 57, 59, 60, 61
Offset: 0

Views

Author

Naohiro Nomoto, Mar 14 2004

Keywords

Links

Crossrefs

Cf. A004086, A030101-A030108, A056960-A056963, A181385.

Programs

  • Mathematica
    rev[x_, b_]:=FromDigits[Reverse[IntegerDigits[x, b]], b]
Length /@ Union /@ Table[Table[rev[x, b], {b, 2, x + 1}], {x, 1, 200}] (* Dylan Hamilton, Oct 16 2010 *)
  • PARI
    a(n) = #Set(apply(b -> fromdigits(Vecrev(digits(n,b)),b), [2..max(2,n+1)])) \\ Rémy Sigrist, Jan 29 2020

A055961 a(n) = n - (reversal of base-11 digits of n) (written in base 10).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, -10, -20, -30, -40, -50, -60, -70, -80, -90, 20, 10, 0, -10, -20, -30, -40, -50, -60, -70, -80, 30, 20, 10, 0, -10, -20, -30, -40, -50, -60, -70, 40, 30, 20, 10, 0, -10, -20, -30, -40, -50, -60, 50, 40, 30, 20, 10, 0, -10, -20, -30, -40, -50, 60, 50, 40, 30, 20, 10, 0, -10, -20, -30, -40
Offset: 0

Views

Author

Henry Bottomley, Jul 18 2000

Keywords

Comments

a(n) is a multiple of 10.

Links

Crossrefs

Cf. A056960 (base-11 reversal), A056965 (n minus decimal reversal).

Programs

  • Maple
    f:= proc(n) local L,t;
  L:= convert(n,base,11);
  n - add(L[-i]*11^(i-1),i=1..nops(L))
end proc:
map(f, [$0..100]); # Robert Israel, Apr 20 2021
  • Mathematica
    Table[n-FromDigits[Reverse[IntegerDigits[n,11]],11],{n,0,80}] (* Harvey P. Dale, Feb 21 2023 *)
  • PARI
    a(n) = n - fromdigits(Vecrev(digits(n, 11)), 11); \\ Michel Marcus, Apr 22 2021

Formula

a(n) = n - A056960(n).

A055960 n + reversal of base 11 digits of n (written in base 10).

Original entry on oeis.org

0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 60, 72, 84, 96, 108, 120, 132, 144
Offset: 0

Views

Author

Henry Bottomley, Jul 18 2000

Keywords

Comments

If n has an even number of digits in base 11 then a(n) is a multiple of 12.

Crossrefs

Cf. A056960, A056964.

Programs

  • Mathematica
    Table[n+IntegerReverse[n,11],{n,0,70}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 30 2016 *)

Formula

a(n) = n + A056960(n).

A091951 Let R_{k}(m) = the digit reversal of m in base k (R_{k}(m) is written in base 10). a(n) is the smallest m such that R_{k}(m) = n, where k >= 2.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 5, 8, 6, 10, 7, 12, 7, 11, 9, 8, 10, 18, 9, 15, 9, 10, 13, 24, 10, 16, 15, 12, 11, 18, 11, 17, 12, 14, 19, 12, 13, 22, 21, 16, 13, 21, 13, 20, 15, 14, 23, 32, 14, 22, 15, 20, 17, 30, 15, 16, 15, 22, 31, 39, 16, 26, 33, 16, 20, 18, 17, 28, 21, 26, 17, 27, 17, 26
Offset: 0

Views

Author

Naohiro Nomoto, Mar 17 2004

Keywords

Crossrefs

Cf. A004086, A030101-A030108, A056960-A056963.

A092122 Let R_{k}(m) = the digit reversal of m in base k (R_{k}(m) is written in base 10). Sequence gives numbers m such that m = Sum_{d|m, d>1} R_{d}(m).

Original entry on oeis.org

6, 154, 310, 370, 2829, 3526, 15320, 20462, 1164789, 4336106, 5782196, 145582972
Offset: 1

Views

Author

Naohiro Nomoto, Mar 30 2004

Keywords

Examples

			m = 154 is a term: Sum_{d|154, d>1} R_{d}(154) = 89 + 10 + 34 + 11 + 7 + 2 + 1 = 154.

Crossrefs

Cf. A004086, A030101-A030108, A056960-A056963.

Programs

  • Python
    from sympy import divisors
from sympy.ntheory import digits
def fd(d, b): return sum(di*b**i for i, di in enumerate(d[::-1]))
def R(k, n): return fd(digits(n, k)[1:][::-1], k)
def ok(n):
    s = 0
    for d in divisors(n, generator=True):
        if d == 1: continue
        s += R(d, n)
        if s > n: return False
    return n == s
print([k for k in range(1, 21000) if ok(k)]) # Michael S. Branicky, Nov 14 2022

Extensions

a(9)-a(12) from Michael S. Branicky, Nov 14 2022

A092358 Let R_{k}(m) = the digit reversal of m in base k (R_{k}(m) is written in base 10). a(n) is the smallest x such that there are exactly n bases {k} (k >= 2 and (x < y)) solutions of the equation: R_{k}(x) = y and R_{k}(y) = x.

Original entry on oeis.org

5, 11, 47, 67
Offset: 1

Views

Author

Naohiro Nomoto, Mar 18 2004

Keywords

Examples

			a(2)=11 because there are two solutions: R_{3}(11) = 19 and R_{3}(19) = 11, R_{9}(11) = 19 and R_{9}(19) = 11.

Crossrefs

Cf. A004086, A030101-A030108, A056960-A056963, A037183, A091974.

A092359 Let R_{k}(m) = the digit reversal of m in base k (R_{k}(m) is written in base 10). a(n) is the smallest y such that there are exactly n bases {k} (k >= 2 and (x < y)) solutions of the equation: R_{k}(x) = y and R_{k}(y) = x.

Original entry on oeis.org

7, 19, 61, 193
Offset: 1

Views

Author

Naohiro Nomoto, Mar 18 2004

Keywords

Examples

			a(2)=19 because there are two solutions: R_{3}(11) = 19 and R_{3}(19) = 11, R_{9}(11) = 19 and R_{9}(19) = 11.

Crossrefs

Cf. A004086, A030101-A030108, A056960-A056963, A037183, A091974.
Showing 1-10 of 11 results. Next

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

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