Search: id:A054735
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%I A054735
%S A054735 8,12,24,36,60,84,120,144,204,216,276,300,360,384,396,456,480,540,564,
%T A054735 624,696,840,864,924,1044,1140,1200,1236,1284,1320,1620,1644,1656,1716,
%U A054735 1764,2040,2064,2100,2124,2184,2304,2460,2556,2580,2604,2640,2856,2904
%N A054735 Sum of twin prime pairs.
%C A054735 (p^q)+(q^p) calculated modulo pq, where (p,q) is the n-th twin prime 
               pair. Example: (599^601)+(601^599) == 1200 mod (599*601). - Sam Alexander 
               (amnalexander(AT)yahoo.com), Nov 14 2003
%C A054735 El'hakk makes the following claim (without any proof): (q^p)+(p^q) == 
               2cosh(q arctanh( sqrt( 1-((2/p)^2) ) )) + 2cosh(p arctanh( sqrt( 
               1-((2/q)^2) ) )) mod pq - Sam Alexander (amnalexander(AT)yahoo.com), 
               Nov 14 2003
%H A054735 El'hakk, <a href="http://www.geocities.com/timeparadox/elhakk.htm">Page 
               of the time traveler</a>
%F A054735 a(n) = 2*A014574(n-1) = 4*A040040(n-1) = A111046(n)/2.
%e A054735 a(3)=24 because the twin primes 11 and 13 add to 24.
%p A054735 ZL:=[]:for p from 1 to 1451 do if (isprime(p) and isprime(p+2)) then 
               ZL:=[op(ZL),p+(p+2)]; fi; od; print(ZL); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Mar 07 2007
%t A054735 Select[Table[Prime[n] + 1, {n, 230}], PrimeQ[ # + 1] &] *2 - Ray Chandler 
               (rayjchandler(AT)sbcglobal.net), Oct 12 2005
%Y A054735 Cf. A001359, A006512, A014574, A040040, A111046.
%Y A054735 Sequence in context: A105571 A141616 A088525 this_sequence A162691 A077566 
               A067677
%Y A054735 Adjacent sequences: A054732 A054733 A054734 this_sequence A054736 A054737 
               A054738
%K A054735 easy,nonn
%O A054735 1,1
%A A054735 Enoch Haga (Enokh(AT)comcast.net), Apr 22 2000
%E A054735 Additional comments from Ray Chandler (rayjchandler(AT)sbcglobal.net), 
               Nov 16 2003

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