A108278 Numbers k such that k^2-1 and k^2+1 are semiprimes.

12, 30, 42, 60, 102, 108, 198, 312, 462, 522, 600, 810, 828, 1020, 1050, 1062, 1278, 1452, 1488, 1872, 1950, 2028, 2130, 2142, 2340, 2790, 2802, 2970, 3000, 3120, 3252, 3300, 3330, 3672, 3930, 4020, 4092, 4230, 4548, 4800, 5280, 5640, 5652, 5658, 6198

Offset: 1

Author

Hugo Pfoertner, May 30 2005

Keywords

• nonn

Comments

Subsequence of A069062. - Michel Marcus, Jan 22 2016

Subsequence of A014574. - Robert Israel, Jan 24 2016

Examples

			a(1)=12 because 12^2-1=143=11*13 and 12^2+1=145=5*29 are both semiprimes.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001358 (semiprimes), A069062 (k^2-1 and k^2+1 have the same number of divisors), A014574 (average of twin prime pairs).

Programs

Magma

IsSemiprime:=func< n | &+[k[2]: k in Factorization(n)] eq 2 >; [ n: n in [4..7000] | IsSemiprime(n^2+1) and IsSemiprime(n^2-1) ]; // Vincenzo Librandi, Jan 22 2016

Maple

filter:= n -> isprime(n+1) and isprime(n-1) and numtheory:-bigomega(n^2+1)=2:
select(filter, [seq(i,i=2..1000, 2)]); # Robert Israel, Jan 24 2016

Mathematica

Select[Range[7000], PrimeOmega[#^2 - 1] == PrimeOmega[#^2 + 1]== 2 &] (* Vincenzo Librandi, Jan 22 2016 *)

PARI

isok(n) = (bigomega(n^2-1) == 2) && (bigomega(n^2+1) == 2); \\ Michel Marcus, Jan 22 2016