A130057 Primes prime(n) such that at least one of the two numbers (prime(n+1)^2-prime(n)^2)/2 - 1 and (prime(n+1)^2-prime(n)^2)/2 + 1 is prime.

3, 5, 7, 11, 13, 17, 19, 23, 29, 37, 41, 43, 53, 61, 67, 73, 89, 97, 103, 109, 137, 139, 163, 167, 179, 181, 191, 197, 199, 227, 239, 241, 251, 257, 263, 269, 277, 281, 283, 293, 307, 313, 331, 353, 359, 367, 379, 397, 409, 419, 421, 431, 433, 443, 449, 463, 479

Offset

1,1

Links

Table of n, a(n) for n=1..57.

Example

a(1)=3 because (5^2 - 3^2)/2 - 1 = 7 and (5^2 - 3^2)/2 + 1 = 9 (7 is prime),
a(2)=5 because (7^2 - 5^2)/2 - 1 = 11 and (7^2 - 5^2)/2 + 1 = 13 (11 and 13 are primes),
a(3)=7 because (11^2 - 7^2)/2 - 1 = 35 and (11^2 - 7^2)/2 + 1 = 37 (37 is prime), ...

Maple

ts_p3:=proc(n) local a, b, i, ans; ans := [ ]: for i from 2 by 1 to n do a := (ithprime(i+1)^(2)-ithprime(i)^(2))/2-1: b := (ithprime(i+1)^(2)-ithprime(i)^(2))/2+1: if (isprime(a)=true or isprime(b)=true) then ans := [ op(ans), ithprime(i) ]: fi od; RETURN(ans) end: ts_p3(200);

Crossrefs

Cf. A130761.

Sequence in context: A007703 A002556 A130101 * A226181 A363286 A120637

Adjacent sequences: A130054 A130055 A130056 * A130058 A130059 A130060

Keyword

nonn

Author

Jani Melik, Aug 01 2007

Status

approved