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A281926 Numbers that are the product of exactly 5 primes and are of the form prime(k) + prime(k + 1).

%I A281926 #19 Mar 11 2024 01:49:32
%S A281926 112,120,162,300,396,450,456,520,630,684,696,702,752,828,882,918,924,
%T A281926 990,1044,1064,1140,1250,1272,1300,1428,1530,1650,1692,1710,1716,1740,
%U A281926 1900,2032,2072,2124,2156
%N A281926 Numbers that are the product of exactly 5 primes and are of the form prime(k) + prime(k + 1).
%C A281926 Note that there is no case of 2 primes.
%C A281926 Intersection of A001043 and A014614. - _Bruno Berselli_, Feb 02 2017
%H A281926 Robert Israel, <a href="/A281926/b281926.txt">Table of n, a(n) for n = 1..10000</a>
%e A281926 112 = 2^4 * 7 = 53 + 59, 120 = 2^3 * 3 * 5 = 59 + 61, 162 = 2 * 3^4 = 79 + 83.
%t A281926 Total[#] & /@ Select[Partition[Prime[Range[1000]], 2, 1], 5 == PrimeOmega[Total[#]] &]
%o A281926 (PARI) list(lim)=my(v=List()); forprime(p=2,lim\16, forprime(q=2,min(lim\(8*p),p), forprime(r=2,min(lim\(4*p*q),q), forprime(s=2,min(lim\(2*p*q*r),r), my(t=2*p*q*r*s); if(nextprime(t/2)+precprime(t/2)==t, listput(v,t)))))); Set(v) \\ _Charles R Greathouse IV_, Feb 05 2017
%Y A281926 Cf. A001043, A014614.
%Y A281926 Cf. A105936 (products of 3 primes), A281925 (products of 4 primes).
%K A281926 nonn
%O A281926 1,1
%A A281926 _Zak Seidov_, Feb 02 2017