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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. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 17 15:35 EDT 2022. Contains 356189 sequences. (Running on oeis4.)