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A081715
Numbers n such that 3^n+2 is a semiprime.
2
6, 7, 11, 12, 20, 27, 28, 40, 44, 60, 71, 84, 108, 118, 145, 156, 160, 211, 263, 295, 296, 304, 306, 316, 351, 474, 488, 495
OFFSET
1,1
COMMENTS
a(29) >= 514. - Hugo Pfoertner, Jul 24 2019
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
EXAMPLE
a(1)=6 because 3^6+2=731=17*43, a(2)=7 because 3^7+2=2189=11*199.
a(1)=6 because 3^6+2=731=17*43
a(2)=7 because 3^7+2=2189=11*199
a(3)=11 because 3^11+2=177149=7*25307
a(4)=12 because 3^12+2=531443=11*48313
a(5)=20 because 3^20+2=3486784403=58027*60089
a(6)=27 because 3^27+2=7625597484989=11*693236134999
a(7)=28 because 3^28+2=22876792454963=131*174632003473
a(8)=40 because 3^40+2=12157665459056928803=1170408739*10387538177
a(9)=44 because 3^44+2=984770902183611232883=21577*45639843452917979
a(10)=60 because 3^60+2=42391158275216203514294433203=89*476305149159732623756117227
a(11)=71 because 3^71+2=7509466514979724803946715958257549=7*1072780930711389257706673708322507
a(12)=84 because 3^84+2=11972515182562019788602740026717047105683=13483993*887905769645684315365837109728331
a(13)=108 because 3^108+2=3381391913522726342930221472392241170198527451848563=671633*5034582746116891729456744192724659405059798211
a(14)=118 because 3^118+2=199667811101603467823686647723289448859052847504205678491=17*11745165358917851048452155748428791109356049853188569323
a(15)=145 because 3^145+2=1522586358169246802159262479225089070726226750574991661790882326344645=5*304517271633849360431852495845017814145245350114998332358176465268929
a(16)=156 because 3^156+2=269721605590607563262106870407286853611938890184108047911269431464974473523=21883136019044570108827*12325546272521124629737118652366725946328428459583049
a(17)=160 because 3^160+2=21847450052839212624230656502990235142567050104912751880812823948662932355203=19*1149865792254695401275297710683696586450897373942776414779622313087522755537
a(18)=211 because 3^211+2=47052721287394587764057094854672253553918218437190874778408030747195017485692977810906266281547645149=97*485079600900975131588217472728579933545548643682380152354721966465928015316422451658827487438635517
a(19)=263 because 3^263+2=304011485348815530556923313708989269910796626718253224787639751028488890841299195402970869140037716024202112537180443065484429=7*43430212192687932936703330529855609987256660959750460683948535861212698691614170771852981305719673717743158933882920437926347
a(20)=295 because 3^295+2=563339419994190847700930153835754386693266237141306322927902016783411511018514718493004963603658195013376479179415613344911575031957595780109=3535513*159337391771488564092659298335419608609349261943402929908022404891004929417177851840172830252259911083165718575894251653129708484159893
PROG
(PARI) for(n=1, 295, if(bigomega(3^n+2)==2, print1(n", "))) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 25 2007
CROSSREFS
KEYWORD
more,hard,nonn
AUTHOR
Hugo Pfoertner, Apr 04 2003
EXTENSIONS
2 more terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 25 2007
More terms from Sean A. Irvine, Mar 21 2010
STATUS
approved