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A263469
Numbers k such that k! + 2^k + 3 or k! + 2^k - 3 is prime.
1
0, 2, 3, 4, 5, 6, 7, 15, 17, 21, 42, 57, 99, 312, 372, 15030
OFFSET
1,2
COMMENTS
Both k! + 2^k + 3 and k! + 2^k - 3 are prime for k = 3 or 4. Are there any others?
No more terms below 10^4. - Charles R Greathouse IV, Nov 17 2015
EXAMPLE
For k = 0, k! + 2^k + 3 = 0! + 2^0 + 3 = 5, which is prime.
For k = 2, k! + 2^k - 3 = 2! + 2^2 - 3 = 3, which is prime.
MATHEMATICA
Select[Range[0, 10^3], Or[PrimeQ[#! + 2^# + 3], PrimeQ[#! + 2^# - 3]] &] (* Michael De Vlieger, Oct 20 2015 *)
PROG
(PARI) for(n=0, 1e3, if(isprime(n!+2^n-3) || isprime(n!+2^n+3), print1(n", ")))
(PARI) is(n)=my(N=n!+2^n); ispseudoprime(N-3) || ispseudoprime(N+3) \\ Charles R Greathouse IV, Nov 17 2015
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Altug Alkan, Oct 19 2015
EXTENSIONS
a(14)-a(15) from Michael De Vlieger, Oct 20 2015
a(16) from Michael S. Branicky, Jul 25 2024
STATUS
approved