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A243153 Larger of two consecutive primes whose difference is a semiprime.

%I A243153 #19 Mar 30 2025 15:33:19
%S A243153 11,17,23,29,37,41,47,53,59,67,71,79,83,89,101,107,113,127,131,137,
%T A243153 149,157,163,167,173,179,191,197,227,233,239,251,257,263,269,277,281,
%U A243153 293,307,311,317,331,337,347,353,359,373,379,383,389,401,419,431,439,443
%N A243153 Larger of two consecutive primes whose difference is a semiprime.
%C A243153 Number of terms less than 10^k: 0, 0, 14, 107, 695, 4927, 37484, 295717, 2413153, ... - _Muniru A Asiru_, Jan 27 2018
%H A243153 K. D. Bajpai, <a href="/A243153/b243153.txt">Table of n, a(n) for n = 1..10000</a>
%e A243153 29 is prime and appears in the sequence because 29 - 23 = 6 = 2 * 3 which is a semiprime.
%e A243153 149 is prime and appears in the sequence because 149 - 139 = 10 = 2 * 5 which is a semiprime.
%p A243153 with(numtheory): A243153:= proc()  ;if bigomega(ithprime(n+1)-ithprime(n))=2 then RETURN (ithprime(n+1)); fi; end: seq(A243153 (), n=1..200);
%t A243153 n = 0; Do[t = Prime[k] - Prime[k - 1]; If [PrimeOmega[t] == 2, n++; Print[n, " ", Prime[k]]], {k, 2, 25000}]
%t A243153 Select[Partition[Prime[Range[100]],2,1],PrimeOmega[#[[2]]-#[[1]]]==2&][[;;,2]] (* _Harvey P. Dale_, Mar 30 2025 *)
%o A243153 (GAP) P := Filtered([1..10^4], IsPrime);;
%o A243153 P1 := List([1..Length(P)-1], i->P[i+1]-P[i]);;
%o A243153 P2:=[];; for i in [1..Length(P1)] do if Number(Factors(P1[i])) = 2 then Add(P2, P[i+1]); fi; od; A243153 := P2; # _Muniru A Asiru_, Jan 27 2018
%Y A243153 Cf. A000040, A001358, A118590, A058620.
%K A243153 nonn
%O A243153 1,1
%A A243153 _K. D. Bajpai_, May 31 2014