A108278 - OEIS

%I #18 Sep 08 2022 08:45:19

%S 12,30,42,60,102,108,198,312,462,522,600,810,828,1020,1050,1062,1278,

%T 1452,1488,1872,1950,2028,2130,2142,2340,2790,2802,2970,3000,3120,

%U 3252,3300,3330,3672,3930,4020,4092,4230,4548,4800,5280,5640,5652,5658,6198

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

%C Subsequence of A069062. - _Michel Marcus_, Jan 22 2016

%C Subsequence of A014574. - _Robert Israel_, Jan 24 2016

%H Robert Israel, <a href="/A108278/b108278.txt">Table of n, a(n) for n = 1..10000</a>

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

%p filter:= n -> isprime(n+1) and isprime(n-1) and numtheory:-bigomega(n^2+1)=2:

%p select(filter, [seq(i,i=2..1000, 2)]); # _Robert Israel_, Jan 24 2016

%t Select[Range[7000], PrimeOmega[#^2 - 1] == PrimeOmega[#^2 + 1]== 2 &] (* _Vincenzo Librandi_, Jan 22 2016 *)

%o (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

%o (PARI) isok(n) = (bigomega(n^2-1) == 2) && (bigomega(n^2+1) == 2); \\ _Michel Marcus_, Jan 22 2016

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

%K nonn

%O 1,1

%A _Hugo Pfoertner_, May 30 2005