A173083 - OEIS

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A173083

Semiprimes q such that q^2+3 and q^2-3 are also semiprimes.

6, 226, 262, 302, 314, 334, 346, 382, 466, 482, 514, 538, 562, 734, 778, 842, 866, 886, 898, 926, 974, 1006, 1046, 1282, 1306, 1318, 1322, 1438, 1466, 1478, 1574, 1622, 1774, 1822, 1838, 1858, 1894, 1994, 2302, 2342, 2446, 2518, 2578, 2582, 2602, 2638

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

OFFSET

1,1

LINKS

Table of n, a(n) for n=1..46.

FORMULA

{A001358(j): A074985(j)-3 in A001358 and A074985(j)+3 in A001358}. [R. J. Mathar, Mar 11 2010]

EXAMPLE

6^2-3=33 = 3*11 and 6^2+3=39 = 3*13 are semiprimes derived from q=6, so q=6 is in the sequence.

MATHEMATICA

f[n_]:=Last/@FactorInteger[n]=={1, 1}||Last/@FactorInteger[n]=={2}; lst={}; Do[If[f[n], a=n^2-3; b=n^2+3; If[f[a]&&f[b], AppendTo[lst, n]]], {n, 8!}]; lst

CROSSREFS

Cf. A001358, A173082

Sequence in context: A223100 A233142 A166502 * A366252 A338297 A084070

Adjacent sequences: A173080 A173081 A173082 * A173084 A173085 A173086

KEYWORD

nonn

AUTHOR

Vladimir Joseph Stephan Orlovsky, Feb 09 2010

EXTENSIONS

Definition rephrased - R. J. Mathar, Mar 11 2010

STATUS

approved