This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A054735 Sum of twin prime pairs. 34

%I

%S 8,12,24,36,60,84,120,144,204,216,276,300,360,384,396,456,480,540,564,

%T 624,696,840,864,924,1044,1140,1200,1236,1284,1320,1620,1644,1656,

%U 1716,1764,2040,2064,2100,2124,2184,2304,2460,2556,2580,2604,2640,2856,2904

%N Sum of twin prime pairs.

%C (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_, Nov 14 2003

%C El'hakk makes the following claim (without any proof): (q^p)+(p^q) = 2*cosh(q arctanh( sqrt( 1-((2/p)^2) ) )) + 2cosh(p arctanh( sqrt( 1-((2/q)^2) ) )) mod p*q - _Sam Alexander_, Nov 14 2003

%C Also: Numbers N such that N/2-1 and N/2+1 both are prime. - _M. F. Hasler_, Jan 03 2013

%C Excluding the first term, all remaining terms have digital root 3, 6 or 9. - _J. W. Helkenberg_, Jul 24 2013

%H Reinhard Zumkeller, <a href="/A054735/b054735.txt">Table of n, a(n) for n = 1..10000</a>

%H El'hakk, <a href="http://web.archive.org/web/http://www.geocities.com/timeparadox/elhakk.htm">Page of the time traveler</a> [Archived copy on web.archive.org, as of Oct 28 2009.]

%F a(n) = 2*A014574(n) = 4*A040040(n) = A111046(n)/2.

%e a(3)=24 because the twin primes 11 and 13 add to 24.

%p 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_, Mar 07 2007

%p A054735 := proc(n)

%p 2*A001359(n)+2;

%p end proc: # _R. J. Mathar_, Jan 06 2013

%t Select[Table[Prime[n] + 1, {n, 230}], PrimeQ[ # + 1] &] *2 (* _Ray Chandler_, Oct 12 2005 *)

%o (PARI) is_A054735(n)={!bittet(n,0)&&isprime(n\2-1)&&isprime(n\2+1)} \\ _M. F. Hasler_, Jan 03 2013

%o (PARI) pp=1;forprime(p=1,1482, if( p==pp+2, print1(p+pp,", ")); pp=p) \\ Following a suggestion by _R. J. Cano_, Jan 05 2013

%o a054735 = (+ 2) . (* 2) . a001359 -- _Reinhard Zumkeller_, Feb 10 2015

%Y Cf. A001359, A006512, A014574, A040040, A111046.

%K easy,nonn

%O 1,1

%A _Enoch Haga_, Apr 22 2000

%E Broken link fixed by _M. F. Hasler_, Jan 03 2013

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 6 21:48 EST 2019. Contains 329809 sequences. (Running on oeis4.)