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 1-3 of 3 results.

A181385 Maximal number that can be obtained by reversing n in an integer base.

Original entry on oeis.org

0, 1, 2, 3, 4, 7, 9, 13, 16, 21, 25, 31, 36, 43, 49, 57, 64, 73, 81, 91, 100, 111, 121, 133, 144, 157, 169, 183, 196, 211, 225, 241, 256, 273, 289, 307, 324, 343, 361, 381, 400, 421, 441, 463, 484, 507, 529, 553, 576, 601, 625, 651, 676, 703, 729, 757, 784, 813, 841
Offset: 0

Views

Author

Dylan Hamilton, Oct 16 2010

Keywords

Comments

The second differences of this sequence start with 2 zeros and then seem to alternate between 2 and -1 perpetually
The bases which yield the first five numbers on this list are {{2},{3},{2,4},{3,5},{3}}, where multiple items on the sublists indicate multiple bases yielding the same maximum. 3 and 4 seem to be the only 2 numbers with multiple bases that yield the same maximum. The numbers of the bases which yield numbers on this list for values n greater than 5 seem to be Floor((n+2)/2).
a(n) agrees with the lower matching number of the (n+1) X (n+1) white bishop graph up to at least n = 13. - Eric W. Weisstein, Dec 23 2024

Links

Crossrefs

Cf. A091974.
Cf. A000982 (ceiling(n^2/2)).
Cf. A002620 (ceiling(n^2/4)).

Programs

  • Mathematica
    rev[x_, b_]:=FromDigits[Reverse[IntegerDigits[x, b]], b]
Max /@ Table[Table[rev[x, b], {b, 2, x + 1}], {x, STARTPOINT, ENDPOINT}]
Table[Piecewise[{{2, n == 2}}, 1/8 (3 - 3 (-1)^n + 2 n^2)], {n, 20}] (* Eric W. Weisstein, Dec 23 2024 *)
Table[Piecewise[{{2, n == 2}}, Ceiling[n^2/2] - Floor[n^2/4]], {n, 20}] (* Eric W. Weisstein, Dec 23 2024 *)
CoefficientList[Series[(-1 + x^2 - 2 x^4 + x^5)/((-1 + x)^3 (1 + x)), {x, 0, 20}], x] (* Eric W. Weisstein, Dec 23 2024 *)
{1, 2} ~ Join ~ LinearRecurrence[{2, 0, -2, 1}, {3, 4, 7, 9}, 20] (* Eric W. Weisstein, Dec 23 2024 *)
  • PARI
    a(n) = vecmax(apply(b -> fromdigits(Vecrev(digits(n,b)),b), [2..max(2,n+1)])) \\ Rémy Sigrist, Jan 29 2020

Formula

a(n) = ceiling(n^2/2) - floor(n^2/4) for n != 2. - Eric W. Weisstein, Dec 23 2024
a(n) = (3 - 3 (-1)^n + 2 n^2)/8 for n != 2. - Eric W. Weisstein, Dec 23 2024
a(n) = 2*a(n-1)-2*a(n-3)+a(n-4) for n > 6. - Eric W. Weisstein, Dec 23 2024
G.f.: x*(-1+x^2-2*x^4+x^5)/((-1+x)^3*(1+x)). - Eric W. Weisstein, Dec 23 2024

Extensions

a(0) = 0 prepended by Rémy Sigrist, Jan 29 2020

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 1-3 of 3 results.

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

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