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A268186
Numbers n such that n^2 + 2, n^2 - 2, n + 2 and n - 2 are all semiprimes.
2
12, 53, 84, 204, 207, 251, 379, 413, 456, 471, 483, 631, 687, 705, 765, 783, 1079, 1135, 1140, 1167, 1269, 1335, 1347, 1395, 1475, 1515, 1587, 1641, 1709, 1767, 1851, 1855, 1943, 1959, 2049, 2157, 2319, 2325, 2575, 2843, 2865, 3099, 3153, 3225, 3267, 3601, 3779
OFFSET
1,1
LINKS
EXAMPLE
12 appears in the sequence because:
12^2 + 2 = 146 = 2*73
12^2 - 2 = 142 = 2*71
12 + 2 = 14 = 2*7
12 - 2 = 10 = 2*5 are all semiprimes.
MAPLE
with(numtheory): select(n -> (bigomega(n^2 + 2)=2 and bigomega(n^2 - 2)=2 and bigomega(n + 2)=2 and bigomega(n - 2)=2), [seq(n, n=1..10000)]);
MATHEMATICA
Select[Range[10000], PrimeOmega[#^2 + 2] == PrimeOmega[#^2 - 2] == PrimeOmega[# + 2] == PrimeOmega[# - 2] == 2 &]
PROG
(PARI) for(n = 1, 10000, if(bigomega(n^2 + 2) == 2 && bigomega(n^2 - 2) == 2 && bigomega(n + 2) == 2 && bigomega(n - 2) == 2, print1(n, ", ")))
(Magma) IsSemiprime:=func<i | &+[d[2]: d in Factorization(i)] eq 2>; [ n : n in [2..10000] | IsSemiprime(n^2 + 2) and IsSemiprime(n^2 - 2) and IsSemiprime(n + 2) and IsSemiprime(n - 2)];
CROSSREFS
KEYWORD
nonn,less
AUTHOR
K. D. Bajpai, Jan 28 2016
STATUS
approved