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%I #10 Nov 06 2020 16:42:05
%S 201658,563866,1213162,2229322,4627534,13593838,29982262,127004446,
%T 318134506,641966518,948880006,1340689846,1671022954,1827766126,
%U 4241032018,6055076206,8775783286,14009110642,19917191062,32482037662,36682577026,43862470342,64900170418
%N Semiprimes of the form prime(n)^3 - prime(n+1)^2.
%C All the terms in the sequence are even.
%H K. D. Bajpai, <a href="/A241060/b241060.txt">Table of n, a(n) for n = 1..8656</a>
%e a(1) = 201658 = 59^3 - 61^2: Also 201658 = 2*100829 (product of two primes). Hence 201658 is semiprime.
%e a(2) = 563866 = 83^3 - 89^2: Also 563866 = 2*281933 (product of two primes). Hence 563866 is semiprime.
%p with(numtheory):KD:= proc() local a,b; a:=ithprime(n)^3 - ithprime(n+1)^2; b:=bigomega(a); if b=2 then RETURN (a); fi; end: seq(KD(), n=1..800);
%t KD = {}; Do[t = Prime[n]^3 - Prime[n + 1]^2; If[PrimeOmega[t] == 2, AppendTo[KD, t]], {n, 500}]; KD
%t n = 0; Do[t = Prime[k]^3 - Prime[k + 1]^2; If[PrimeOmega[t] == 2, n = n + 1; Print[n, " ", t]], {k, 1, 500000}]
%t Select[#[[1]]^3-#[[2]]^2&/@Partition[Prime[Range[600]],2,1],PrimeOmega[ #] == 2&] (* _Harvey P. Dale_, Nov 06 2020 *)
%o (PARI) s=[]; for(n=1, 10000, t=prime(n)^3-prime(n+1)^2; if(bigomega(t)==2, s=concat(s, t))); s \\ _Colin Barker_, Apr 16 2014
%Y Cf. A001358, A005898, A046388, A240859, A240884.
%K nonn
%O 1,1
%A _K. D. Bajpai_, Apr 15 2014
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