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

1,1

Links

Table of n, a(n) for n=1..56.

Example

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), ...

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);

Crossrefs

Cf. A130761.

Sequence in context: A045404 A154500 A152460 * A020612 A072539 A062391

Adjacent sequences: A130094 A130095 A130096 * A130098 A130099 A130100

Keyword

nonn

Author

Jani Melik, Aug 01 2007

Status

approved