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A173087 Semiprimes k such that k^2 - 7 and k^2 + 7 are also semiprime. 0
82, 142, 214, 254, 326, 358, 386, 478, 538, 542, 566, 674, 758, 802, 974, 1198, 1366, 1466, 1594, 1754, 1762, 1942, 2302, 2342, 2374, 2582, 2654, 2746, 2762, 2818, 2998, 3106, 3134, 3418, 3494, 3518, 3554, 3566, 3646, 3734, 3778, 3862, 4138, 4178, 4258 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..45.

EXAMPLE

82 = 2*41, 82^2 - 7 = 6717 = 3*2239 and 82^2 + 7 = 6731 = 53*127 are all semiprime, hence 82 is a term.

MATHEMATICA

f[n_]:=Last/@FactorInteger[n]=={1, 1}||Last/@FactorInteger[n]=={2}; lst={}; Do[If[f[n], a=n^2-7; b=n^2+7; If[f[a]&&f[b], AppendTo[lst, n]]], {n, 8!}]; lst

PROG

(MAGMA) IsSemiprime:=func< n | &+[ k[2]: k in Factorization(n) ] eq 2 >; [ n: n in [2..4300] | IsSemiprime(n) and IsSemiprime(n^2-7) and IsSemiprime(n^2+7) ]; // Klaus Brockhaus, Feb 25 2010

CROSSREFS

Cf. A001358, A173082, A173083, A173084, A173085, A173086.

Sequence in context: A039547 A029704 A260835 * A264352 A044252 A044633

Adjacent sequences:  A173084 A173085 A173086 * A173088 A173089 A173090

KEYWORD

nonn

AUTHOR

Vladimir Joseph Stephan Orlovsky, Feb 09 2010

EXTENSIONS

Edited by Klaus Brockhaus and N. J. A. Sloane, Feb 25 2010

STATUS

approved

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Last modified August 25 13:50 EDT 2019. Contains 326324 sequences. (Running on oeis4.)