Search: id:A099497
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%I A099497
%S A099497 5,7,8,11,17,18,21,23,25,27,32,47,51,56,59,165
%N A099497 Numbers n such that A007925(n)=n^(n+1)-(n+1)^n is a semiprime.
%C A099497 a(15)=59 confirmed by the factorization of 59^60-60^59, which is the 
               product of the 52-digit prime 1994803969065168661575061125592557043358338451845483 
               and the 55-digit prime 8529249434913526091880095870250840825853220069057672947. 
               The next term is > 150.
%H A099497 Dario Alpern, <a href="http://www.alpertron.com.ar/ECM.HTM">Factorization 
               using the Elliptic Curve Method.</a>
%H A099497 Jason Papadopoulos, <a href="http://www.boo.net/~jasonp/qs.html">MSIEVE: 
               A Library for Factoring Large Integers.</a>
%e A099497 a(1)=5 because 5^6-6^5=7849=47*167 is a semiprime.
%e A099497 a(1) = 5 because 5^6-6^5 = 47*167
%e A099497 a(2) = 7 because 7^8-8^7 = 23*159463
%e A099497 a(3) = 8 because 8^9-9^8 = 257*354751
%e A099497 a(4) = 11 because 11^12-12^11 = 33479*71549927
%e A099497 a(5) = 17 because 17^18-18^17 = 443881*26757560905578361
%e A099497 a(6) = 18 because 18^19-19^18 = 100417*6015993258685545623
%e A099497 a(7) = 21 because 21^22-22^21 = 10745792197529*9973660056412561
%e A099497 a(8) = 23 because 23^24-24^23 = 92798617729*4576344458074395243073
%e A099497 a(9) = 25 because 25^26-26^25 = 1627*1219220786258356172077730898121187
%e A099497 a(10) = 27 because 27^28-28^27 = 12298336501553*877252504725615101634783073
%e A099497 a(11) = 32 because 32^33-33^32 = 3506869732968391733353*12220478717670771804763962407
%e A099497 a(12) = 47 because 47^48-48^47 = 11*1562101337142488025295723727786855927046203814783168243784058499133923137\
               7934499
%e A099497 a(13) = 51 because 51^52-52^51 = 10562756058978342869988055703171*5575962824795589360993690554534422732411612\
               977322491058843
%e A099497 a(14) = 56 because 56^57-57^56 = 5*84398033416966745730297080637651148292094863554029064321397352391471503651\
               8308339240201775858865907
%e A099497 a(15) = 59 because 59^60-60^59 = 1994803969065168661575061125592557043358338451845483*85292494349135260918800\
               95870250840825853220069057672947
%e A099497 a(16) = 165 because 165^166-166^165 = 7633959407*163076907868213615950266217178793475613011504837818623396515\
               564012661893226303732651906966725064757412175602397914466548918056488078725366468844166112514226848566007\
               329847679870618316491448786496781907628093854483627149015842065338540933592790765847673522595877456839311\
               59999248465944943129517543272252180930134912057221968601458271001580745436226192252814407
%Y A099497 Cf. A007925 n^(n+1)-(n+1)^n, A072179 n^(n+1)-(n+1)^n is prime, A099498 
               semiprimes of the form n^(n+1)-(n+1)^n.
%Y A099497 Sequence in context: A082728 A154370 A045251 this_sequence A061813 A047384 
               A066001
%Y A099497 Adjacent sequences: A099494 A099495 A099496 this_sequence A099498 A099499 
               A099500
%K A099497 hard,nonn
%O A099497 1,1
%A A099497 Hugo Pfoertner (hugo(AT)pfoertner.org), Oct 19 2004, Aug 13 2007
%E A099497 165 from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 12 2008

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