OFFSET
1,1
COMMENTS
All the terms in the sequence are even.
LINKS
K. D. Bajpai, Table of n, a(n) for n = 1..8656
EXAMPLE
a(1) = 201658 = 59^3 - 61^2: Also 201658 = 2*100829 (product of two primes). Hence 201658 is semiprime.
a(2) = 563866 = 83^3 - 89^2: Also 563866 = 2*281933 (product of two primes). Hence 563866 is semiprime.
MAPLE
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);
MATHEMATICA
KD = {}; Do[t = Prime[n]^3 - Prime[n + 1]^2; If[PrimeOmega[t] == 2, AppendTo[KD, t]], {n, 500}]; KD
n = 0; Do[t = Prime[k]^3 - Prime[k + 1]^2; If[PrimeOmega[t] == 2, n = n + 1; Print[n, " ", t]], {k, 1, 500000}]
Select[#[[1]]^3-#[[2]]^2&/@Partition[Prime[Range[600]], 2, 1], PrimeOmega[ #] == 2&] (* Harvey P. Dale, Nov 06 2020 *)
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
K. D. Bajpai, Apr 15 2014
STATUS
approved