cp's OEIS Frontend

A077065 Semiprimes of form prime - 1.

%I A077065 #53 Jul 20 2023 07:20:39
%S A077065 4,6,10,22,46,58,82,106,166,178,226,262,346,358,382,466,478,502,562,
%T A077065 586,718,838,862,886,982,1018,1186,1282,1306,1318,1366,1438,1486,1522,
%U A077065 1618,1822,1906,2026,2038,2062,2098,2206,2446,2458,2578,2818,2878,2902
%N A077065 Semiprimes of form prime - 1.
%C A077065 There are 670 semiprimes of form prime-1 below 10^5.
%H A077065 Vincenzo Librandi, <a href="/A077065/b077065.txt">Table of n, a(n) for n = 1..1000</a>
%F A077065 a(n) = A005385(n) - 1 = 2*A005384(n).
%F A077065 A010051(A006093(a(n))/2) = A064911(A006093(a(n))) = 1. - _Reinhard Zumkeller_, Nov 22 2013
%F A077065 a(n) = A077068(n) - A232342(n). - _Reinhard Zumkeller_, Dec 16 2013
%F A077065 a(n) = A000010(A194593(n+1)). - _Torlach Rush_, Aug 23 2018
%F A077065 A000010((a(n)*2)+2) = A023900((a(n)*2)+2). - _Torlach Rush_, Aug 23 2018
%e A077065 A001358(16) = 46 = 2*23 is a term as 46 = A000040(15) - 1 = 47 - 1.
%p A077065 q:= n-> (n::even) and andmap(isprime, [n+1, n/2]):
%p A077065 select(q, [$1..5000])[];  # _Alois P. Heinz_, Jul 19 2023
%t A077065 Select[Range[6000],Plus@@Last/@FactorInteger[#]==2&&PrimeQ[#+1]&] (* _Vladimir Joseph Stephan Orlovsky_, May 08 2011 *)
%t A077065 Select[Range[3000],PrimeOmega[#]==2&&PrimeQ[#+1]&] (* _Harvey P. Dale_, Oct 16 2012 *)
%t A077065 Select[ Prime@ Range@ 430 - 1, PrimeOmega@# == 2 &] (* _Robert G. Wilson v_, Feb 18 2014 *)
%o A077065 (Magma) IsSemiprime:=func<n | &+[d[2]: d in Factorization(n)] eq 2>; [s: n in [2..500] | IsSemiprime(s) where s is NthPrime(n)-1]; // _Vincenzo Librandi_, Oct 17 2012
%o A077065 (Haskell)
%o A077065 a077065 n = a077065_list !! (n-1)
%o A077065 a077065_list = filter ((== 1) . a010051' . (`div` 2)) a006093_list
%o A077065 -- _Reinhard Zumkeller_, Nov 22 2013, Oct 27 2012
%o A077065 (PARI) [x-1|x<-primes(10^4),bigomega(x-1)==2] \\ _Charles R Greathouse IV_, Nov 22 2013
%Y A077065 Intersection of A006093 and A001358.
%Y A077065 Intersection of A006093 and A100484.
%Y A077065 Cf. A077068, A232342, A064911.
%Y A077065 Cf. A005384, A005385.
%Y A077065 Cf. A000010, A023900, A194593.
%K A077065 nonn
%O A077065 1,1
%A A077065 _Reinhard Zumkeller_, Oct 23 2002