|
%I #15 Jan 09 2019 01:54:30
%S 5,13,17,103,197,227,787,823,911,919,1153,1409,1487,1723,2087,2647,
%T 2767,2999,3001,3389,6089,6781,6827,7877,9463,10391,10789,11117,11447,
%U 11971,13523,13537,13711,13807,14087,14489,16063,18191,21059,23371,25717
%N Primes p such that (p + nextprime + p) and also (p + previousprime + p) are primes.
%C First pairs of two successive primes in the sequence are {13, 17}, {911, 919}, {2999, 3001} (twin primes!), {13523, 13537}, {52543, 52553}.
%C First case of three successive primes is {78059, 78079, 78101}.
%H Robert Israel, <a href="/A125146/b125146.txt">Table of n, a(n) for n = 1..10000</a>
%e 13 is a term because 13 + 17 + 13 = 43 and 13 + 11 + 13 = 37 are primes.
%p Primes:= select(isprime, [2,seq(i,i=3..10^5,2)]):
%p Primes[select(t -> isprime(2*Primes[t]+Primes[t-1]) and isprime(2*Primes[t]+Primes[t+1]), [$2..nops(Primes)-1])]; # _Robert Israel_, Mar 15 2018
%t pQ[n_]:=PrimeQ[2n+NextPrime[n]]&&PrimeQ[2n+NextPrime[n,-1]]; Select[ Prime[Range[2,3000]],pQ] (* _Harvey P. Dale_, Apr 25 2011 *)
%K nonn
%O 1,1
%A _Zak Seidov_, Jan 11 2007
|
