A130090 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 not prime.

3, 7, 11, 17, 19, 23, 31, 37, 41, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313

Offset

1,1

Comments

The value (prime(n+1)^2-prime(n)^2)/2 must be an integer.

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 (9 is not prime),
a(2)=7 because (11^2 - 7^2)/2 - 1 = 35 and (11^2 - 7^2)/2 + 1 = 37 (35 is not prime),
a(3)=11 because (13^2 - 11^2)/2 - 1 = 23 and (13^2 - 11^2)/2 + 1 = 25 (25 is not prime), ...

Maple

ts_p3_20:=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 not (isprime(a)=true and isprime(b)=true) then ans := [ op(ans), ithprime(i) ]: fi od; RETURN(ans) end: ts_p3_20(300);

Mathematica

npQ[n_]:=Module[{x=(Last[n]^2-First[n]^2)/2}, IntegerQ[x]&&MemberQ[ PrimeQ[ {x+1, x-1}], False]]; Transpose[Select[Partition[Prime[ Range[80]], 2, 1], npQ]][[1]] (* Harvey P. Dale, May 07 2011 *)

Crossrefs

Cf. A130761.

Sequence in context: A023211 A038981 A065376 * A136059 A156284 A045419

Adjacent sequences: A130087 A130088 A130089 * A130091 A130092 A130093

Keyword

nonn

Author

Jani Melik, Aug 01 2007

Status

approved