A064278 Numbers k such that k! + prime(k) is prime.

1, 2, 3, 4, 5, 6, 9, 11, 17, 18, 25, 31, 40, 96, 174, 193, 204, 269, 523, 650, 659, 797, 1437, 1862, 2515, 4983, 5557, 11429

Offset

1,2

Comments

The numbers corresponding to 2515 and 4983 are probable primes. [Farideh Firoozbakht, Oct 15 2009]

a(28) > 10000. - Giovanni Resta, Mar 16 2014

Links

Table of n, a(n) for n=1..28.

Example

n=5: 5! = 120 and prime(5) = 11, 120+11 = 131.
6 is listed because 6!+prime(6) = 720+13 = 733 is prime.

Mathematica

Do[ If[ PrimeQ[ n! + Prime[ n ] ], Print[ n ] ], {n, 1, 700} ]
Select[Range[1000], PrimeQ[#! + Prime[#]] &] (* Vincenzo Librandi, Mar 05 2015 *)

Prog

(PARI) for(n=1, 100, if (isprime(n!+prime(n)), print1(n, ", ")))
(Magma) [n: n in [1..200] | IsPrime(Factorial(n)+ NthPrime(n))]; // Vincenzo Librandi, Mar 05 2015

Crossrefs

Cf. A063499 (Primes of form prime(n) + n!). [Alexander R. Povolotsky, Aug 13 2008]

Sequence in context: A364698 A102571 A251241 * A220570 A341057 A299297

Adjacent sequences: A064275 A064276 A064277 * A064279 A064280 A064281

Keyword

nonn

Author

Jason Earls, Sep 24 2001

Extensions

More terms from Robert G. Wilson v, Sep 28 2001

More terms from John Sillcox (JMS21187(AT)aol.com), Apr 05 2003

a(25)-a(26) from Farideh Firoozbakht, Oct 15 2009

a(27) from Giovanni Resta, Mar 16 2014

a(28) from Michael S. Branicky, Sep 22 2024

Status

approved