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.

A178576 Primes that are the sum of two Fibonacci numbers.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 23, 29, 37, 47, 89, 97, 149, 157, 199, 233, 241, 379, 521, 613, 631, 1021, 1597, 1741, 2207, 3571, 9349, 10949, 11933, 17713, 28657, 46381, 46457, 46601, 50549, 75169, 196439, 203183, 214129, 514229, 560597, 832129, 2178343
Offset: 1

Views

Author

Carmine Suriano, Jan 12 2011

Keywords

Comments

The corresponding prime indices are in A178971.

Examples

			Prime 613 can be expressed as 3+610 = Fibonacci(4)+Fibonacci(15), therefore 613 is in the sequence.

Links

Crossrefs

Cf. A000040, A000045, A178971. Subsequence of A059389.

Programs

  • Mathematica
    f=Fibonacci[Range[33]]; Select[Union[Flatten[Outer[Plus, f, f]]], PrimeQ]
  • PARI
    list(lim)={
    my(v,u=List(),t);
    v=vector(log(lim*sqrt(5))\log((1+sqrt(5))/2)+1,n,fibonacci(n));
    for(i=1,#v,for(j=i+1,#v,
        t = v[i] + v[j];
        if(t > lim, break);
        if(ispseudoprime(t),listput(u, t))
    ));
    vecsort(Vec(u),,8)
}; \\ Charles R Greathouse IV, Jul 23 2012

A178977 a(n) = (3*n+2)*(3*n+5)/2.

Original entry on oeis.org

5, 20, 44, 77, 119, 170, 230, 299, 377, 464, 560, 665, 779, 902, 1034, 1175, 1325, 1484, 1652, 1829, 2015, 2210, 2414, 2627, 2849, 3080, 3320, 3569, 3827, 4094, 4370, 4655, 4949, 5252, 5564, 5885, 6215, 6554, 6902, 7259, 7625, 8000, 8384, 8777, 9179, 9590, 10010
Offset: 0

Views

Author

Paul Curtz, Jan 02 2011

Keywords

Comments

Companion to A145910.

Links

Crossrefs

Cf. A008585, A145910, A168233, A168300, A016789, A178971, A235332.

Programs

Formula

a(n) = a(n-1) + 6 + 9*n.
a(n) = A178971(3*n+2).
a(n) = A145910(n) + 3 + 3*n = A145910(n) + A008585(n+1).
a(n) = A168233(n+1)*A168300(n+1).
G.f.: (-5-5*x+x^2)/(x-1)^3. [Adapted to the offset by Bruno Berselli, Apr 14 2011]
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Apr 19 2013
From Amiram Eldar, Mar 10 2022: (Start)
Sum_{n>=0} 1/a(n) = 1/3.
Sum_{n>=0} (-1)^n/a(n) = 4*Pi/(9*sqrt(3)) - 1/3 - 4*log(2)/9. (End)
From Elmo R. Oliveira, Oct 30 2024: (Start)
E.g.f.: exp(x)*exp(x)*(5 + 15*x + 9*x^2/2).
a(n) = A016789(n)*A016789(n+1)/2. (End)

A178978 a(n) = A144448(n+1)/8.

Original entry on oeis.org

0, 2, 5, 1, 14, 20, 1, 35, 44, 2, 65, 77, 10, 104, 119, 5, 152, 170, 7, 209, 230, 28, 275, 299, 4, 350, 377, 5, 434, 464, 55, 527, 560, 22, 629, 665, 26, 740, 779, 91, 860, 902, 35, 989, 1034, 40, 1127, 1175, 136, 1274, 1325, 17
Offset: 0

Views

Author

Paul Curtz, Jan 02 2011

Keywords

Comments

Differs from A178971 for indices n > 23.

Links

Crossrefs

Cf. A061039, A145910, A145911, A178971, A178977, A178978, A144448.

Programs

Formula

Trisections:
a(3*n) = A145911(n);
a(3*n+1) = A145910(n);
a(3*n+2) = A178977(n).
a(n) = 3*a(n-27) - 3*a(n-54) + a(n-81). - G. C. Greubel, Mar 06 2022
Showing 1-3 of 3 results.

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

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