A268186 Numbers n such that n^2 + 2, n^2 - 2, n + 2 and n - 2 are all semiprimes.

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

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