A217357 - OEIS

%I #19 Mar 15 2024 02:25:28

%S 32777,88649,91799,113107,165697,273257,310103,322211,326137,460963,

%T 466063,468877,480443,483223,506509,509131,553349,564347,565493,

%U 587611,616771,623257,624959,625619,739177,766799,777163,826657,832357,834123,845177,860873,916163

%N Semiprimes p such that next semiprime after p is p+30.

%C Smallest difference between two consecutive terms occurs first at a(329) = 5861197 because a(330) = 5861227 and 5861227 - 5861197 = 30. Same difference for a(1212) = 16179703, a(1630) = 20611897 and a(1641) = 20703923.- _Zak Seidov_, Feb 14 2017

%H Zak Seidov, <a href="/A217357/b217357.txt">Table of n, a(n) for n = 1..1000</a>

%e 32777 =A001358(8112)  = 73*449, 32807 = A001358(8113) = 3*619,

%e 88649 =A001358(20880)  = 11*8059, 88679 = A001358(20881) = 71*1249.

%t Select[Partition[Select[Range[10^6],PrimeOmega[#]==2&],2,1],#[[2]]-#[[1]] == 30&][[All,1]] (* _Harvey P. Dale_, May 06 2022 *)

%o (Magma) IsSemiprime:=func<n | &+[d[2]: d in Factorization(n)] eq 2>; [n: n in [4..1000000] | IsSemiprime(n) and IsSemiprime(n+30) and forall{n+i: i in [1..29] | not IsSemiprime(n+i)}]; // _Bruno Berselli_, Oct 01 2012

%Y Cf. A001358, A065516, A217030, A217335.

%K nonn

%O 1,1

%A _Zak Seidov_, Oct 01 2012