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

5, 7, 11, 17, 19, 23, 29, 31, 41, 53, 61, 67, 71, 79, 83, 101, 109, 139, 149, 157, 163, 197, 211, 229, 271, 281, 283, 293, 311, 337, 347, 349, 379, 389, 401, 409, 431, 449, 457, 463, 467, 491, 499, 509, 547, 617, 641, 653, 659, 661, 701, 719, 743, 751, 757

Offset: 1

Author

Amarnath Murthy, Aug 11 2002

Keywords

• nonn

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..10000 (terms 1..2000 from Harry J. Smith)

Crossrefs

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

Programs

Magma

[NthPrime(n): n in [0..200] | IsPrime(NthPrime(n)+NthPrime(n+1)+ NthPrime(n+2))]; // Vincenzo Librandi, May 06 2015

Maple

t0:=[];
t1:=[];
t2:=[];
for i from 1 to 1000 do
t3:=ithprime(i)+ithprime(i+1)+ithprime(i+2);
if isprime(t3) then
t0:=[op(t0),i];
t1:=[op(t1),ithprime(i)];
t2:=[op(t2),ithprime(i+2)];
fi;
od:
t1;

Mathematica

Transpose[Select[Partition[Prime[Range[200]],3,1],PrimeQ[Total[#]]&]] [[1]] (* Harvey P. Dale, Jan 25 2012 *)

PARI

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

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

Formula

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

Extensions

More terms from Ralf Stephan, Mar 20 2003

More cross-references from Harvey P. Dale, Jun 05 2013