A080798
Largest prime factor of 3^n-2.
Original entry on oeis.org
7, 5, 79, 241, 727, 23, 937, 19681, 431, 499, 4703, 8093, 40193, 2869781, 483671, 94747, 4657, 232452293, 498112057, 2812679, 31381059607, 3765727153, 1364071, 44594137339, 125231, 13170403, 5353801183, 4159349, 46050353857, 294487079, 26892769, 29178816413, 3533781113
Offset: 2
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[Max(PrimeDivisors(3^n-2)):n in [2..30]]; // Marius A. Burtea, Jul 12 2019
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FactorInteger[#][[-1,1]]&/@(3^Range[2,30]-2) (* Harvey P. Dale, Apr 07 2022 *)
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a(n) = vecmax(factor(3^n-2)[,1]); \\ Michel Marcus, Jul 12 2019
A081715
Numbers n such that 3^n+2 is a semiprime.
Original entry on oeis.org
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
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
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for(n=1, 295, if(bigomega(3^n+2)==2, print1(n", "))) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 25 2007
2 more terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 25 2007
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