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 1-8 of 8 results.

A047904 a(n+1) = a(n) + n (if n is odd), a(n+1) = a(n) * n (if n is even).

Original entry on oeis.org

1, 2, 4, 7, 28, 33, 198, 205, 1640, 1649, 16490, 16501, 198012, 198025, 2772350, 2772365, 44357840, 44357857, 798441426, 798441445, 15968828900, 15968828921, 351314236262, 351314236285, 8431541670840, 8431541670865, 219220083442490
Offset: 1

Views

Author

Miklos SZABO (mike(AT)ludens.elte.hu)

Keywords

Crossrefs

Programs

  • Haskell
    a047904 n = a047904_list !! (n-1)
    a047904_list = 1 : zipWith uncurry
                               (cycle [(+), (*)]) (zip a047904_list [1..])
    -- Reinhard Zumkeller, Nov 13 2013, Mar 24 2013
  • Mathematica
    Transpose[NestList[{#[[1]]+1,If[OddQ[#[[1]]],Total[#],Times@@#]}&,{1,1},30]][[2]] (* Harvey P. Dale, Sep 11 2012 *)
  • Python
    a=1
    for n in range(1,33):
        print(a, end=", ")
        if n&1:
            a += n
        else:
            a *= n
    # Alex Ratushnyak, Feb 24 2013
    

A047905 a(n+1) = a(n) + n (if n is even), a(n+1) = a(n) * n (if n is odd).

Original entry on oeis.org

1, 1, 3, 9, 13, 65, 71, 497, 505, 4545, 4555, 50105, 50117, 651521, 651535, 9773025, 9773041, 166141697, 166141715, 3156692585, 3156692605, 66290544705, 66290544727, 1524682528721, 1524682528745, 38117063218625, 38117063218651
Offset: 1

Views

Author

Miklos SZABO (mike(AT)ludens.elte.hu)

Keywords

Crossrefs

Programs

  • Haskell
    a047905 n = a047905_list !! (n-1)
    a047905_list = 1 : zipWith uncurry
                               (cycle [(*), (+)]) (zip a047905_list [1..])
    -- Reinhard Zumkeller, Nov 13 2013, May 31 2011
    
  • Mathematica
    a[0]=1;a[n_]:=a[n]=If[EvenQ[n],a[n-1]+n,a[n-1]n];Join[{1}, Array[a,40]] (* Harvey P. Dale, Apr 24 2011 *)
    nxt[{n_,a_}]:={n+1,If[EvenQ[n],a+n,a*n]}; NestList[nxt,{1,1},30][[All,2]] (* Harvey P. Dale, Jul 27 2021 *)
  • Python
    a=1
    for n in range(1,33):
        print(a, end=", ")
        if n&1:
            a *= n
        else:
            a += n
    # Alex Ratushnyak, Feb 24 2013

A222559 a(0) = 0. If n is odd, a(n) = a(n-1) * n, otherwise a(n) = a(n-1) + n.

Original entry on oeis.org

0, 0, 2, 6, 10, 50, 56, 392, 400, 3600, 3610, 39710, 39722, 516386, 516400, 7746000, 7746016, 131682272, 131682290, 2501963510, 2501963530, 52541234130, 52541234152, 1208448385496, 1208448385520, 30211209638000, 30211209638026, 815702660226702, 815702660226730
Offset: 0

Views

Author

Alex Ratushnyak, Feb 24 2013

Keywords

Crossrefs

Programs

  • Mathematica
    last = 0; Table[If[OddQ[n], last = n * last, last = n + last], {n, 0, 40}] (* T. D. Noe, Mar 01 2013 *)
    nxt[{n_,a_}]:={n+1,If[EvenQ[n],a(n+1),a+n+1]}; NestList[nxt,{0,0},30][[All,2]] (* Harvey P. Dale, May 14 2019 *)
  • Python
    a=0
    for n in range(1,33):
        print(a, end=',')
        if n&1:
            a *= n
        else:
            a += n

A093302 a(n) = (a(n-1)+(2n-1))*(2n) with a(0) = 0.

Original entry on oeis.org

0, 2, 20, 150, 1256, 12650, 151932, 2127230, 34035920, 612646866, 12252937700, 269564629862, 6469551117240, 168208329048890, 4709833213369676, 141294996401091150, 4521439884834917792, 153728956084387206050
Offset: 0

Views

Author

Emrehan Halici (emrehan(AT)halici.com.tr), Apr 24 2004

Keywords

Crossrefs

a(n) = A007566(n)-1 = 2*A010844(n)-2n-2. Bisection of A077138.
Cf. A271476.

Programs

  • Mathematica
    RecurrenceTable[{a[0]==0,a[n]==(a[n-1]+2n-1)2n},a,{n,20}] (* Harvey P. Dale, May 20 2014 *)
  • PARI
    a(n)=2*floor(exp(1/2)*n!*2^n)-2*n-2
    
  • PARI
    x='x+O('x^99); concat(0, Vec(serlaplace((2*x+4*x^2)/(1-2*x)*exp(x)))) \\ Altug Alkan, Aug 01 2018
    
  • PARI
    a=vector(99); a[1]=2; for(n=2, #a, a[n] = 2*(a[n-1]+2*n-1)*n); concat(0,a) \\ Altug Alkan, Aug 01 2018

Formula

a(n) = 2 * floor(e^(1/2) * n! * 2^n) - 2n - 2.
E.g.f.: (2x+4x^2)/(1-2x) * exp(x).
a(n) = 2*A271476(n) for n >= 1. - Altug Alkan, Aug 01 2018

Extensions

Edited by Ralf Stephan, Apr 26 2004

A332657 Alternate adding and multiplying prime numbers: a(2n) = a(2n-1) * prime(2n+1) and a(2n-1) = a(2n) + prime(2n-2) for n >= 1.

Original entry on oeis.org

5, 25, 32, 352, 365, 6205, 6224, 143152, 143181, 4438611, 4438648, 181984568, 181984611, 8553276717, 8553276770, 504643329430, 504643329491, 33811103075897, 33811103075968, 2468210524545664, 2468210524545743, 204861473537296669, 204861473537296758
Offset: 1

Views

Author

Adnan Baysal, Feb 18 2020

Keywords

Examples

			a(1) = 2 + 3 = 5;
a(2) = 5 * 5 = 25;
a(3) = 25 + 7 = 32;
...
a(40) = 2714410084880275101596278688487175846.
		

Crossrefs

Programs

  • Python
    from sympy import primerange
    p = list(primerange(1, 200))
    def a(n):
        out = p[0] + p[1]
        for i in range(1, n):
            if i % 2:
                out *= p[i + 1]
            else:
                out += p[i + 1]
        return out
    for n in range(1, 25):
        print(a(n), end=", ")

A332659 Alternate multiplying and adding prime numbers: a(2n) = a(2n-1) + prime(2n+1) and a(2n-1) = a(2n) * prime(2n-2) for n >= 1.

Original entry on oeis.org

6, 11, 77, 88, 1144, 1161, 22059, 22082, 640378, 640409, 23695133, 23695174, 1018892482, 1018892529, 54001304037, 54001304096, 3294079549856, 3294079549923, 233879648044533, 233879648044606, 18476492195523874, 18476492195523957, 1644407805401632173
Offset: 1

Views

Author

Adnan Baysal, Feb 18 2020

Keywords

Examples

			a(1) =  2 * 3 =  6;
a(2) =  6 + 5 = 11;
a(3) = 11 * 7 = 77.
		

Crossrefs

Programs

  • Python
    from sympy import primerange
    p = list(primerange(1, 1000))
    def a(n):
        out = p[0] * p[1]
        for i in range(1, n):
            if i % 2:
                out += p[i + 1]
            else:
                out *= p[i + 1]
        return out

A332660 Alternate adding and multiplying Fibonacci numbers: a(0) = F(0) + F(1), for n >= 0, a(2n+1) = a(2n) * F(2n+2), a(2n+2) = a(2n+1) + F(2n+3).

Original entry on oeis.org

1, 1, 3, 9, 14, 112, 125, 2625, 2659, 146245, 146334, 21072096, 21072329, 7944268033, 7944268643, 7840993150641, 7840993152238, 20261126305382992, 20261126305387173, 137066519455944225345
Offset: 0

Views

Author

Adnan Baysal, Feb 18 2020

Keywords

Examples

			a(0) = 0 + 1 =  1;
a(1) = 1 * 1 =  1;
a(2) = 1 + 2 =  3;
a(3) = 3 * 3 =  9;
a(4) = 9 + 5 = 14.
		

Crossrefs

Programs

  • Mathematica
    a[0] = 1; a[n_] := a[n] = If[OddQ[n], a[n-1] * Fibonacci[n+1], a[n-1] + Fibonacci[n+1]]; Array[a, 20, 0] (* Amiram Eldar, Mar 28 2020 *)
  • Python
    from sympy import fibonacci
    f = [fibonacci(n) for n in range(100)]
    def a(n):
        out = f[0] + f[1]
        for i in range(1, n):
            if i%2:
                out *= f[i+1]
            else:
                out += f[i+1]
        return out

A333591 Alternate multiplying and adding Fibonacci numbers: a(0) = F(0) * F(1), for n >= 0, a(2n+1) = a(2n) + F(2n+2), a(2n+2) = a(2n+1) * F(2n+3).

Original entry on oeis.org

0, 1, 2, 5, 25, 33, 429, 450, 15300, 15355, 1366595, 1366739, 318450187, 318450564, 194254844040, 194254845027, 310224987508119, 310224987510703, 1297050672782249243, 1297050672782256008, 14197516664274574263568, 14197516664274574281279
Offset: 0

Views

Author

Adnan Baysal, Mar 27 2020

Keywords

Examples

			a(0) = 0 * 1 =  0;
a(1) = 0 + 1 =  1;
a(2) = 1 * 2 =  2;
a(3) = 2 + 3 =  5;
a(4) = 5 * 5 = 25.
		

Crossrefs

Programs

  • Mathematica
    a[0] = 0; a[n_] := a[n] = If[EvenQ[n], a[n-1] * Fibonacci[n+1], a[n-1] + Fibonacci[n+1]]; Array[a, 22, 0] (* Amiram Eldar, Mar 28 2020 *)
  • Python
    from sympy import fibonacci
    f = [fibonacci(n) for n in range(200)]
    def a(n):
        out = f[0] * f[1]
        for i in range(1, n+1):
            if i%2:
                out += f[i+1]
            else:
                out *= f[i+1]
        return out
Showing 1-8 of 8 results.