A081715 Numbers n such that 3^n+2 is a semiprime.

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

Author

Hugo Pfoertner, Apr 04 2003

Keywords

• more
• hard
• nonn

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

Examples

			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
		

Links

• Status of 3^514+2 in factordb.com.

Crossrefs

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

Programs

PARI

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

Extensions

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

More terms from Sean A. Irvine, Mar 21 2010