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

2, 3, 6, 14, 30, 35, 37, 39, 41, 46, 52, 57, 68, 81, 82, 97, 101, 104, 112, 123, 126, 145, 154, 175, 189, 195, 209, 215, 221, 222, 259, 264, 272, 276, 308, 312, 314, 343, 357, 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

Offset: 1

Author

Zak Seidov, Apr 11 2014

Keywords

• nonn

Comments

a(n) = position of A216432(n) in A069484.

Examples

			a(1) = 2: prime (2)^2 + prime (3)^2  = 3^2 + 5^2 = 34 = A069484(2) = A216432 (1).
a(2) = 3: prime (3)^2 + prime (4)^2  = 5^2 + 7^2 = 74 = A069484(3)  = A216432 (2).
a(3) = 6: prime (6)^2 + prime (7)^2  = 13^2 + 17^2 = 458 = A069484(6)  = A216432 (3).
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A069484, A216432.

Programs

Maple

with(numtheory):
isok := n -> evalb(bigomega(ithprime(n)^2 + ithprime(n+1)^2) = 2);
A240749_list := n -> select(isok, [$1..n]); A240749_list(555); # Peter Luschny, Apr 12 2014

Mathematica

Position[Total/@Partition[Prime[Range[600]]^2,2,1],?(PrimeOmega[#] == 2&)]// Flatten (* _Harvey P. Dale, Apr 12 2017 *)

PARI

isok(n) = bigomega(prime(n)^2  + prime(n+1)^2) == 2;
lista(nn) = {for(n=1, nn, if (isok(n), print1(n, ", ")));} \\ Michel Marcus, Apr 12 2014

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