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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

%I

%S 3,7,11,17,19,23,31,37,41,47,53,59,61,67,71,73,79,83,89,97,101,107,

%T 109,113,127,131,137,139,149,151,157,173,179,181,191,193,197,199,211,

%U 223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313

%N 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.

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

%e a(1)=3 because (5^2 - 3^2)/2 - 1 = 7 and (5^2 - 3^2)/2 + 1 = 9 (9 is not prime),

%e a(2)=7 because (11^2 - 7^2)/2 - 1 = 35 and (11^2 - 7^2)/2 + 1 = 37 (35 is not prime),

%e a(3)=11 because (13^2 - 11^2)/2 - 1 = 23 and (13^2 - 11^2)/2 + 1 = 25 (25 is not prime), ...

%p 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);

%t 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],2,1],npQ]][] (* _Harvey P. Dale_, May 07 2011 *)

%Y Cf. A130761.

%K nonn

%O 1,1

%A _Jani Melik_, Aug 01 2007

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Last modified September 27 22:01 EDT 2022. Contains 357063 sequences. (Running on oeis4.)