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.

A076513 Numbers k such that 2 + 2^k + 3^k is prime.

Original entry on oeis.org

1, 3, 5, 65, 119, 213, 1209, 2469, 2669, 3939, 11219
Offset: 1

Views

Author

Zak Seidov, Oct 17 2002

Keywords

Comments

119, 213, 1209 and 2469 proved prime by Primo v1.2.1. - Robert G. Wilson v Oct 17 2002
a(12) > 10^5. - Giovanni Resta, Mar 19 2014

Crossrefs

Cf. A075996.

Programs

  • Mathematica
    Do[ If[ PrimeQ[2 + 2^n + 3^n], Print[n]], {n, 1, 4000, 2}]
    Select[Range[10000], PrimeQ[2 + 2^# + 3^#] &] (* _Vincenzo Librandi: Oct 05 2012 *)
  • PARI
    is(n)=ispseudoprime(2+2^n+3^n) \\ Charles R Greathouse IV, Jun 13 2017

Extensions

Edited and extended by Robert G. Wilson v, Oct 17 2002
a(10) from Vincenzo Librandi, Oct 05 2012
a(11) from Giovanni Resta, Feb 19 2013

A173657 2+2^n+3^n.

Original entry on oeis.org

4, 7, 15, 37, 99, 277, 795, 2317, 6819, 20197, 60075, 179197, 535539, 1602517, 4799355, 14381677, 43112259, 129271237, 387682635, 1162785757, 3487832979, 10462450357, 31385253915, 94151567437, 282446313699, 847322163877, 2541932937195, 7625731702717
Offset: 0

Views

Author

Gary Detlefs, Nov 24 2010

Keywords

Comments

Sum of the n-th powers of the first 5 Fibonacci numbers A000045(0..4).

Crossrefs

Cf. A075996 (primes), A007689.

Programs

  • Maple
    with(combinat):f:=n-> sum(fibonacci(k)^n,k=0..4):seq(f(n),n=1..20);
  • Mathematica
    Table[2+2^n+3^n,{n,0,40}] (* or *) LinearRecurrence[{6,-11,6},{4,7,15},40](* Harvey P. Dale, Jun 08 2011 *)

Formula

a(n)= 6*a(n-1)-11*a(n-2)+6*a(n-3).
a(n) = 1+A001550(n).
G.f.: ( -4+17*x-17*x^2 ) / ( (x-1)*(3*x-1)*(2*x-1) ).

Extensions

More terms from Harvey P. Dale, Jun 08 2011

A353102 Primes of the form 2^k + 3^k + 6.

Original entry on oeis.org

11, 19, 41, 103, 281, 6823, 20201, 14381681, 387682639, 94151567441, 282446313703, 5559069156490121, 16677198879535759, 50031579458738081, 984770919775797277303, 1144561273440060866922804472241, 969773729787523912361831763509149540341223, 2909321189362571427600485469182379896242601
Offset: 1

Views

Author

Hemjyoti Nath, Apr 23 2022

Keywords

Comments

Conjecture: There are infinitely many primes of the form 2^k + 3^k + 6.

Examples

			2^1 + 3^1 + 6 = 11, which is a prime.
2^2 + 3^2 + 6 = 19, which is a prime.
		

Crossrefs

Cf. A075996.

Programs

  • Mathematica
    Select[Table[2^n + 3^n + 6,{n,1,1000}],PrimeQ]
Showing 1-3 of 3 results.