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A073681 Smallest of three consecutive primes whose sum is a prime. 18

%I #52 Sep 07 2023 04:52:22

%S 5,7,11,17,19,23,29,31,41,53,61,67,71,79,83,101,109,139,149,157,163,

%T 197,211,229,271,281,283,293,311,337,347,349,379,389,401,409,431,449,

%U 457,463,467,491,499,509,547,617,641,653,659,661,701,719,743,751,757

%N Smallest of three consecutive primes whose sum is a prime.

%H Hugo Pfoertner, <a href="/A073681/b073681.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..2000 from Harry J. Smith)

%F Conjecture: for n -> oo, a(n) ~ prime(n) * (log(prime(n)))^C, where C = 8/Pi^2 (cf. A217739). - _Alain Rocchelli_, Sep 04 2023

%p t0:=[];

%p t1:=[];

%p t2:=[];

%p for i from 1 to 1000 do

%p t3:=ithprime(i)+ithprime(i+1)+ithprime(i+2);

%p if isprime(t3) then

%p t0:=[op(t0),i];

%p t1:=[op(t1),ithprime(i)];

%p t2:=[op(t2),ithprime(i+2)];

%p fi;

%p od:

%p t1;

%t Transpose[Select[Partition[Prime[Range[200]],3,1],PrimeQ[Total[#]]&]] [[1]] (* _Harvey P. Dale_, Jan 25 2012 *)

%o (PARI) forprime(p=1,1000, pp=nextprime(p+1); if(isprime(p+pp+nextprime(pp+1)),print1(p",")))

%o (PARI) A073681(n,print_all=0,start=3)={my(r,q=1);forprime(p=start,, isprime(r+(r=q)+(q=p)) & (n-- ||return(precprime(r-1))) & print_all & print1(precprime(r-1)","))} \\ _M. F. Hasler_, Dec 18 2012

%o (Magma) [NthPrime(n): n in [0..200] | IsPrime(NthPrime(n)+NthPrime(n+1)+ NthPrime(n+2))]; // _Vincenzo Librandi_, May 06 2015

%Y Cf. A152469, A152470, A174742, A034962, A152468, A180948, A189571, A180950, A226380.

%K nonn

%O 1,1

%A _Amarnath Murthy_, Aug 11 2002

%E More terms from _Ralf Stephan_, Mar 20 2003

%E More cross-references from _Harvey P. Dale_, Jun 05 2013

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Last modified March 28 16:34 EDT 2024. Contains 371254 sequences. (Running on oeis4.)