cp's OEIS Frontend

A240749 Numbers n such that prime(n)^2 + prime(n+1)^2 is a semiprime.

%I A240749 #24 Apr 12 2017 04:43:19
%S A240749 2,3,6,14,30,35,37,39,41,46,52,57,68,81,82,97,101,104,112,123,126,145,
%T A240749 154,175,189,195,209,215,221,222,259,264,272,276,308,312,314,343,357,
%U A240749 367,370,373,389,398,399,403,411,416,418,425,432,436,447,456,462,471,473,477,485,487,489,499,509,520,538,547
%N A240749 Numbers n such that prime(n)^2 + prime(n+1)^2 is a semiprime.
%C A240749 a(n) = position of A216432(n) in A069484.
%H A240749 Zak Seidov, <a href="/A240749/b240749.txt">Table of n, a(n) for n = 1..10000</a>
%e A240749 a(1) = 2: prime (2)^2 + prime (3)^2  = 3^2 + 5^2 = 34 = A069484(2) = A216432 (1).
%e A240749 a(2) = 3: prime (3)^2 + prime (4)^2  = 5^2 + 7^2 = 74 = A069484(3)  = A216432 (2).
%e A240749 a(3) = 6: prime (6)^2 + prime (7)^2  = 13^2 + 17^2 = 458 = A069484(6)  = A216432 (3).
%p A240749 with(numtheory):
%p A240749 isok := n -> evalb(bigomega(ithprime(n)^2 + ithprime(n+1)^2) = 2);
%p A240749 A240749_list := n -> select(isok, [$1..n]); A240749_list(555); # _Peter Luschny_, Apr 12 2014
%t A240749 Position[Total/@Partition[Prime[Range[600]]^2,2,1],_?(PrimeOmega[#] == 2&)]// Flatten (* _Harvey P. Dale_, Apr 12 2017 *)
%o A240749 (PARI) isok(n) = bigomega(prime(n)^2  + prime(n+1)^2) == 2;
%o A240749 lista(nn) = {for(n=1, nn, if (isok(n), print1(n, ", ")));} \\ _Michel Marcus_, Apr 12 2014
%o A240749 (PARI) s=[]; for(n=2, 600, if(isprime((prime(n)^2+prime(n+1)^2)/2), s=concat(s, n))); s \\ _Colin Barker_, Apr 12 2014
%Y A240749 Cf. A069484, A216432.
%K A240749 nonn
%O A240749 1,1
%A A240749 _Zak Seidov_, Apr 11 2014