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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

K. D. Bajpai, Table of n, a(n) for n = 1..3379

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

Subsequence of A105571.

Cf. A001358, A086005, A096173, A096175, A105571, A124936, A237037, A268043.

Sequence in context: A248135 A307916 A280660 * A253130 A213549 A211060

Adjacent sequences:  A268183 A268184 A268185 * A268187 A268188 A268189

KEYWORD

nonn,less

AUTHOR

K. D. Bajpai, Jan 28 2016

STATUS

approved

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Last modified September 22 13:48 EDT 2021. Contains 347607 sequences. (Running on oeis4.)