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 1-5 of 5 results.

A077138 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, 1, 2, 5, 20, 25, 150, 157, 1256, 1265, 12650, 12661, 151932, 151945, 2127230, 2127245, 34035920, 34035937, 612646866, 612646885, 12252937700, 12252937721, 269564629862, 269564629885, 6469551117240, 6469551117265, 168208329048890
Offset: 0

Views

Author

Amarnath Murthy, Oct 30 2002

Keywords

Crossrefs

Programs

  • Mathematica
    a = 0; Table[If[OddQ[n], a = n + a, a = n*a], {n, 0, 30}] (* T. D. Noe, Feb 26 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, Feb 13 2022 *)
  • PARI
    a(n)=if(n<0,0,if(n%2,n+a(n-1),n*a(n-1)))
    
  • Python
    a=0
    for n in range(1, 33):
        print(a, end=', ')
        if n&1:
            a += n
        else:
            a *= n

Formula

a(0) = 0, a(2n) = 2n*a(2n-1) and a(2n+1) = a(2n) +(2n +1).

Extensions

Name improved by T. D. Noe, Feb 26 2013

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 1-5 of 5 results.