A174408 Primes of the form A174335(i)-1 or A174335(i)+1.
17, 257, 2591, 2593, 239999, 2488319, 27659519, 27659521, 330301441, 4232632319, 58060799999, 13243436236801, 70614415872000001, 3429209878281350809286344704000001, 1665505492033205854772229590583093971095149084672000000001
Offset: 1
Examples
a(1) = 17 = 16 * 1^3 * 1! + 1 is prime. a(2) = 257 = 16 * 2^3 * 2! + 1 is prime. a(3) = 2591 = 16 * 3^3 * 3! - 1 is prime. a(4) = 2593 = 16 * 3^3 * 3! + 1 is prime. a(5) = 239999 = 16 * 5^3 * 5! - 1 is prime. a(6) = 2488319 = 16 * 6^3 * 6! - 1 is prime. a(7) = 27659519 = 16 * 7^3 * 7! - 1 is prime. a(8) = 27659521 = 16 * 7^3 * 7! + 1 is prime. a(9) = 330301441 = 16 * 8^3 * 8! + 1 is prime. a(10) = 4232632319 = 16 * 9^3 * 9! - 1 is prime. a(11) = 58060799999 = 16 * 10^3 * 10! - 1 is prime. a(12) = 13243436236801 = 16 * 12^3 * 12! + 1 is prime. a(13) = 70614415872000001 = 16 * 15^3 * 15! + 1 is prime.
Programs
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Maple
A174335 := proc(n) 16*n^3*n! ; end proc: for i from 1 to 60 do a := A174335(i) ; if isprime(a-1) then printf("%d,",a-1) ; end if; if isprime(a+1) then printf("%d,",a+1) ; end if; end do: # R. J. Mathar, Apr 15 2010
Formula
a(n) = {A000040(i)} INTERSECTION ({16*(j^3)*(j!) - 1} UNION {16*(k^3)*(k!) - 1}).
Extensions
One more term from R. J. Mathar, Apr 15 2010