A081715 - OEIS

%I #20 Sep 09 2024 13:43:50

%S 6,7,11,12,20,27,28,40,44,60,71,84,108,118,145,156,160,211,263,295,

%T 296,304,306,316,351,474,488,495

%N Numbers n such that 3^n+2 is a semiprime.

%C a(29) >= 514. - _Hugo Pfoertner_, Jul 24 2019

%C 531, 562, 676, 760, 807, 866, 1059, 1502, 1659, 2539, 2656, 3070, 3163, 4014, 5736, 5966, 6680, 6745, 7192, 7861, 8104, 9703, 10014 are terms of this sequence. - _Chai Wah Wu_, Oct 18 2019

%H <a href="http://factordb.com/index.php?query=3%5E514%2B2">Status of 3^514+2 in factordb.com</a>.

%e a(1)=6 because 3^6+2=731=17*43, a(2)=7 because 3^7+2=2189=11*199.

%e a(1)=6 because 3^6+2=731=17*43

%e a(2)=7 because 3^7+2=2189=11*199

%e a(3)=11 because 3^11+2=177149=7*25307

%e a(4)=12 because 3^12+2=531443=11*48313

%e a(5)=20 because 3^20+2=3486784403=58027*60089

%e a(6)=27 because 3^27+2=7625597484989=11*693236134999

%e a(7)=28 because 3^28+2=22876792454963=131*174632003473

%e a(8)=40 because 3^40+2=12157665459056928803=1170408739*10387538177

%e a(9)=44 because 3^44+2=984770902183611232883=21577*45639843452917979

%e a(10)=60 because 3^60+2=42391158275216203514294433203=89*476305149159732623756117227

%e a(11)=71 because 3^71+2=7509466514979724803946715958257549=7*1072780930711389257706673708322507

%e a(12)=84 because 3^84+2=11972515182562019788602740026717047105683=13483993*887905769645684315365837109728331

%e a(13)=108 because 3^108+2=3381391913522726342930221472392241170198527451848563=671633*5034582746116891729456744192724659405059798211

%e a(14)=118 because 3^118+2=199667811101603467823686647723289448859052847504205678491=17*11745165358917851048452155748428791109356049853188569323

%e a(15)=145 because 3^145+2=1522586358169246802159262479225089070726226750574991661790882326344645=5*304517271633849360431852495845017814145245350114998332358176465268929

%e a(16)=156 because 3^156+2=269721605590607563262106870407286853611938890184108047911269431464974473523=21883136019044570108827*12325546272521124629737118652366725946328428459583049

%e a(17)=160 because 3^160+2=21847450052839212624230656502990235142567050104912751880812823948662932355203=19*1149865792254695401275297710683696586450897373942776414779622313087522755537

%e a(18)=211 because 3^211+2=47052721287394587764057094854672253553918218437190874778408030747195017485692977810906266281547645149=97*485079600900975131588217472728579933545548643682380152354721966465928015316422451658827487438635517

%e a(19)=263 because 3^263+2=304011485348815530556923313708989269910796626718253224787639751028488890841299195402970869140037716024202112537180443065484429=7*43430212192687932936703330529855609987256660959750460683948535861212698691614170771852981305719673717743158933882920437926347

%e a(20)=295 because 3^295+2=563339419994190847700930153835754386693266237141306322927902016783411511018514718493004963603658195013376479179415613344911575031957595780109=3535513*159337391771488564092659298335419608609349261943402929908022404891004929417177851840172830252259911083165718575894251653129708484159893

%o (PARI) for(n=1, 295, if(bigomega(3^n+2)==2, print1(n", "))) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 25 2007

%Y Cf. A001358, A051783, A057735, A080443, A080892.

%K more,hard,nonn

%O 1,1

%A _Hugo Pfoertner_, Apr 04 2003

%E 2 more terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 25 2007

%E More terms from _Sean A. Irvine_, Mar 21 2010