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.

User: Kausthub Gudipati

Kausthub Gudipati's wiki page.

Kausthub Gudipati has authored 102 sequences. Here are the ten most recent ones:

A198516 Largest lifetime of any configuration starting from n cells which are bishop-connected for the cell automaton defined in A198514.

Original entry on oeis.org

1, 2, 3, 6, 6, 8, 9, 10, 14, 17, 17, 20
Offset: 1

Author

Kausthub Gudipati, Oct 26 2011

Keywords

Crossrefs

A198515 Largest lifetime of any configuration starting from n cells which are king-wise connected for the cell automaton defined in A198514.

Original entry on oeis.org

1, 3, 11, 16, 22, 31, 30, 35, 39, 43
Offset: 1

Author

Kausthub Gudipati, Oct 26 2011

Keywords

Examples

			Solution for n=2
33
3123
3213
33
		

Crossrefs

A198514 Consider a cellular automaton on the square grid where we start at time 1 with a finite collection of cells in state 1 and with all cells in state 0. At any time t, if a cell is in state 0 and the sum of the states of its neighborhood is t, the cell switches to state t. At any time t, if no cell switches to state t, the growth stops. The sequence gives the largest lifetime of any configuration starting from n cells which are rook connected.

Original entry on oeis.org

1, 3, 6, 9, 11, 22, 22, 23, 29, 29, 35, 36, 36
Offset: 1

Author

Kausthub Gudipati, Oct 26 2011

Keywords

Examples

			The solution for n=4
  9 9
85 4 58
32 23
6311136
313
74 47
  8
		

Crossrefs

A196509 Largest palindrome formed by using n single-digit numbers and the operators +, -, * and / where concatenation is not allowed.

Original entry on oeis.org

9, 11, 343, 747, 6556, 65856, 405504, 4251524, 8847488
Offset: 1

Author

Kausthub Gudipati, Oct 03 2011

Keywords

Comments

This puzzle is easily trivial if exponentiation or concatenation is allowed.
Best known results for a(10)..a(15) are 88499488, 846747648, 4095995904, 23613431632, 68899199886, 633498894336.
Erich Friedman solved and proved most of these terms.

Examples

			11 = 9 + 2
343 = 7 * 7 * 7
747 = 9 * (9 * 9 + 2)
6556 = 9 * 9 * 9 * 9 - 5
65856 = 3 * 7 * 7 * 8 * 8 * 8
405504 = 8 * 8 * 8 * 8 * 9 * (9 + 2)
4251524 = 8 * 9 * 9 * 9 * 9 * 9 * 9 - 4
8847488 = 8 * 8 * (5 * 6 * 8 * 8 * 8 * 9 + 2)
		

Crossrefs

Cf. A002113.

A196580 Length of longest possible 72-degree snake inside a circle of diameter n.

Original entry on oeis.org

57, 81, 77, 111, 91, 146, 120
Offset: 5

Author

Kausthub Gudipati, Oct 04 2011

Keywords

Comments

A snake is a sequence of unit line segments that are non-overlapping except that each one begins where the previous one ends. An n-degree snake is a snake all of whose multiples with the horizontal are multiples of n.

A196592 Maximum number of floors with n elevators and 3 stops.

Original entry on oeis.org

3, 3, 4, 5, 5, 6, 7, 7, 7, 7, 8, 9, 9, 9, 9, 9
Offset: 1

Author

Kausthub Gudipati, Oct 04 2011

Keywords

References

  • David Rhee and Jerry Lo, Mathematical Wizardy for A Gardener, pp. 165-173.

Extensions

Corrected Name: elevators and stops were interchanged. - Robert Price, May 30 2013

A196594 Maximum number of floors with 4 elevators and s stops.

Original entry on oeis.org

4, 4, 6, 6, 7, 8, 8, 9, 10, 10
Offset: 1

Author

Kausthub Gudipati, Oct 04 2011

Keywords

References

  • David Rhee and Jerry Lo, Mathematical Wizardy for A Gardener, pp. 165-173.

A196520 Smallest Friedman number of order n.

Original entry on oeis.org

25, 279936, 31381059609, 1125899906842624, 1152921504606846976, 4722366482869645213696, 42391158275216203514294433201, 324518553658426726783156020576256
Offset: 1

Author

Kausthub Gudipati, Oct 03 2011

Keywords

Comments

More terms from a=9 to a=12 are 22528399544939174411840147874772641, 147808829414345923316083210206383297601, 1427247692705959881058285969449495136382746624 and 91343852333181432387730302044767688728495783936.

Examples

			Since 25 is the smallest Friedman number, it is the smallest Friedman number of order 1.
279936 = 6^7 = (9 - 3)^(9 - 2), together using the digits of the number itself. Hence it is the smallest Friedman number of order 2.
31381059609 = 9^11 = 9^(5+6) = 3^(30-8+0), together using the digits of the number itself. Hence it is the smallest Friedman number of order 3.
		

Crossrefs

Formula

All numbers of this kind are perfect powers.

A195897 Number of ways to place a queen, a rook, a bishop, a knight and a king on an n X n chessboard such that each piece attacks the same number of unoccupied spaces.

Original entry on oeis.org

28, 39, 90, 63, 64, 197, 15, 7, 5, 1
Offset: 4

Author

Kausthub Gudipati, Sep 25 2011

Keywords

Examples

			There are 64 ways to place 5 different chess pieces on an 8 X 8 chessboard with the above condition.
An example for a 4 X 4 board is
  ...Q
  ..NK
  B...
  R...
		

A196024 Odious Fibonacci numbers.

Original entry on oeis.org

1, 2, 8, 13, 21, 55, 233, 1597, 4181, 28657, 121393, 196418, 317811, 1346269, 2178309, 3524578, 9227465, 165580141, 1134903170, 1836311903, 2971215073, 20365011074, 32951280099, 53316291173, 225851433717, 2504730781961, 6557470319842, 17167680177565, 27777890035288
Offset: 1

Author

Kausthub Gudipati, Sep 27 2011

Keywords

Comments

Intersection of A000069 (odious numbers) and A000045 (Fibonacci numbers).
The k-th Fibonacci number is odious for k = 1, 2, 3, 6, 7, 10, 13, 17, 19, 23, 26, 27, 28, 30, 31, 32, 33, 35, 41, 45, ...
The k-th odious number is a Fibonacci number for k = 1, 2, 5, 7, 11, 28, 117, 799, 2091, ...

Examples

			8 is a Fibonacci number that equals 1000 in binary, which contains one (odd number) 1.
		

Crossrefs

Programs

  • Maple
    isA000069 := proc(n)
            type(wt(n),'odd') ;
    end proc:
    for n from 1 to 300 do
            F := combinat[fibonacci](n) ;
            if isA000069(F) then printf("%d,",F) ; end if;
    end do: # R. J. Mathar, Oct 15 2011
  • Mathematica
    Rest[Select[Fibonacci[Range[100]],OddQ[DigitCount[#,2,1]]&]] (* Harvey P. Dale, Oct 16 2011 *)