OFFSET
1,1
COMMENTS
(1/4)*(n^5 - 133*n^4 + 6729*n^3 - 158379*n^2 + 1720294*n - 6823316) is a well known prime producing polynomial found by Shyam Sunder Gupta, which generates 57 distinct primes for n = 0,1,...,55,56.
For n = 57, this polynomial yields the first semiprime: 5141923 = 821 * 6263.
LINKS
K. D. Bajpai, Table of n, a(n) for n = 1..10000
EXAMPLE
For n=57: (1/4)*(n^5 - 133*n^4 + 6729*n^3 - 158379*n^2 + 1720294*n - 6823316) = 5141923 = 821 * 6263, which is a semiprime and is included in the sequence.
For n=58: (1/4)*(n^5 - 133*n^4 + 6729*n^3 - 158379*n^2 + 1720294*n - 6823316) = 6084557 = 131 * 46447, which is a semiprime and is included in the sequence.
MAPLE
with(numtheory): KD:= proc() local a, b, k; k:=(1/4)*(n^5 - 133*n^4 + 6729*n^3 - 158379*n^2 + 1720294*n - 6823316); a:=bigomega(k); if a=2 then RETURN (k); fi; end: seq(KD(), n=0..200);
MATHEMATICA
A241607 = {}; Do[k= (1/4) * (n^5 - 133 * n^4 + 6729 * n^3 - 158379 * n^2 + 1720294 * n - 6823316); If[PrimeOmega[k] ==2, AppendTo[A241607, k]], {n, 200}]; A241607
(*For the b-file:*) n=0; Do[t=((1/4) * (k^5 - 133 * k^4 + 6729 * k^3 - 158379 * k^2 + 1720294 * k - 6823316)); If[PrimeOmega[t]==2, n++; Print[n, " ", t]], {k, 10^6}]
PROG
(PARI) s=[]; for(n=1, 200, t=(1/4)*(n^5-133*n^4+6729*n^3-158379*n^2+1720294*n-6823316); if(bigomega(t)==2, s=concat(s, t))); s \\ Colin Barker, Apr 26 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
K. D. Bajpai, Apr 26 2014
STATUS
approved