A264046 - OEIS

%I #10 Dec 24 2023 16:25:19

%S 15,123,365,371,505,545,573,591,649,707,807,843,943,1067,1159,1247,

%T 1357,1405,1529,1555,1633,1739,1745,1829,1843,1897,1909,1985,2149,

%U 2159,2209,2285,2329,2353,2363,2407,2413,2463,2501,2643,2773,2779

%N Numbers k such that k and k+6 are consecutive semiprimes.

%C Note that a(1) = 15 = A131109(k=6).

%H Charles R Greathouse IV, <a href="/A264046/b264046.txt">Table of n, a(n) for n = 1..10000</a>

%e 15 = A001358(6) and 21 = A001358(7).

%t Select[Partition[Select[Range[3000],PrimeOmega[#]==2&],2,1],#[[2]]-#[[1]]==6&][[;;,1]] (* _Harvey P. Dale_, Dec 24 2023 *)

%o (PARI) is(n)=if(bigomega(n)!=2 || bigomega(n+6)!=2, return(0)); for(i=1,5,if(bigomega(n+i)==2, return(0))); 1 \\ _Charles R Greathouse IV_, Nov 02 2015

%Y Cf. A001358, A065516, A123375, A131109, A136196, A264043, A264044, A264045.

%K nonn

%O 1,1

%A _Zak Seidov_, Nov 02 2015