A086005 -id:A086005 - cp's OEIS frontend

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

K. D. Bajpai, Jan 28 2016

			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.

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

Subsequence of A105571.

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

IsSemiprime:=func;[ n : n in [2..10000] | IsSemiprime(n^2 + 2) and  IsSemiprime(n^2 - 2) and  IsSemiprime(n + 2) and  IsSemiprime(n - 2)];

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 &]

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, ", ")))

A115394 List of triples of semiprimes: each three numbers are consecutive semiprimes.

Original entry on oeis.org

33, 34, 35, 85, 86, 87, 93, 94, 95, 121, 122, 123, 141, 142, 143, 201, 202, 203, 213, 214, 215, 217, 218, 219, 301, 302, 303, 393, 394, 395, 445, 446, 447, 633, 634, 635, 697, 698, 699, 841, 842, 843, 921, 922, 923, 1041, 1042, 1043, 1137, 1138, 1139, 1261

Offset: 1

Zak Seidov, Mar 08 2006

nonn

Cf. A056809, A086005, A086006.

Flatten[Select[Partition[Union[Times@@@Tuples[Prime[Range[150]],{2}]],3,1],#[[3]]-#[[2]]==#[[2]]-#[[1]]==1&]]  (* Harvey P. Dale, Jan 22 2011 *)

a(3n-2) = A056809(n), a(3n-1) = A086005(n), a(3n) = A086005(n) + 1 = 2*A086006(n) + 1, n=1,2,...

A086007 Number of semiprime triples <= n.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3

Offset: 1

Reinhard Zumkeller, Jul 07 2003

nonn

A semiprime triple is <= n if its least member is <= n;

if a(n-1)A086005(a(n))=n+1.

Cf. A001358, A056809, A086005.

cp's OEIS Frontend

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

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PARI

A115394 List of triples of semiprimes: each three numbers are consecutive semiprimes.

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A086007 Number of semiprime triples <= n.

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