A130097 Primes prime(n) such that at least one of the two numbers (prime(n+2)^2-prime(n)^2)/2 - 1 and (prime(n+2)^2-prime(n)^2)/2 + 1 is not prime.

3, 5, 11, 13, 17, 23, 29, 31, 41, 43, 47, 53, 59, 73, 79, 83, 89, 101, 103, 109, 113, 131, 137, 139, 149, 151, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337

Offset: 1

Author

Jani Melik, Aug 01 2007

Keywords

• nonn

Examples

			a(1)=3 because (7^2 - 3^2)/2 - 1 = 19 and (7^2 - 3^2)/2 + 1 = 21 (21 is not prime),
a(2)=5 because (11^2 - 5^2)/2 - 1 = 47 and (11^2 - 5^2)/2 + 1 = 49 (49 is not prime),
a(3)=11 because (17^2 - 11^2)/2 - 1 = 83 and (17^2 - 11^2)/2 + 1 = 85 (85 is not prime), ...
		

Crossrefs

Cf. A130761.

Programs

Maple

ts_p2_20:=proc(n) local a,b,i,ans; ans := [ ]: for i from 2 to n do a := (ithprime(i+2)^(2)-ithprime(i)^(2))/2-1: b := (ithprime(i+2)^(2)-ithprime(i)^(2))/2+1: if not (isprime(a)=true and isprime(b)=true) then ans := [ op(ans), ithprime(i) ]: fi od; RETURN(ans) end: ts_p2_20(300);