A241060 Semiprimes of the form prime(n)^3 - prime(n+1)^2.
201658, 563866, 1213162, 2229322, 4627534, 13593838, 29982262, 127004446, 318134506, 641966518, 948880006, 1340689846, 1671022954, 1827766126, 4241032018, 6055076206, 8775783286, 14009110642, 19917191062, 32482037662, 36682577026, 43862470342, 64900170418
Offset: 1
Keywords
Examples
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.
Links
- K. D. Bajpai, Table of n, a(n) for n = 1..8656
Programs
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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);
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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 *) -
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
Comments