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A094933 Primes prime(k) such that (prime(k-1) + prime(k+1) + prime(k+2))/prime(k) = 3.

%I A094933 #18 Sep 08 2022 08:45:13
%S A094933 127,149,431,967,1031,1061,1597,2437,2833,2953,3793,5923,6449,6701,
%T A094933 6959,7103,8803,11467,11617,11717,11923,12611,13291,13327,13397,13679,
%U A094933 13721,14533,14713,15787,16087,17417,17921,18539,20021,21269,21467,22027
%N A094933 Primes prime(k) such that (prime(k-1) + prime(k+1) + prime(k+2))/prime(k) = 3.
%H A094933 Robert Israel, <a href="/A094933/b094933.txt">Table of n, a(n) for n = 1..10000</a>
%e A094933 127 is OK since 127 is p(31) and (p(n-1) + p(n+1)+ p(n+2))/p(n)=(113+131+137)/127=3. - _Zak Seidov_, Aug 04 2006
%p A094933 p:= 2: q:= 3: r:= 5: s:= 7:
%p A094933 count:= 0: Res:= NULL:
%p A094933 while count < 100 do
%p A094933   if p + r + s = 3*q then count:= count+1; Res:= Res, q fi;
%p A094933   p:= q; q:= r; r:= s; s:= nextprime(s)
%p A094933 od:
%p A094933 Res; # _Robert Israel_, May 06 2019
%t A094933 a=Table[If[(Prime[n-3]+Prime[n-2]+Prime[n-1]+Prime[n])/4-Prime[n-2]==0, Prime[n-2], 0], {n, 4, 2004}] a0=Delete[Union[Sort[a]], 1]
%t A094933 Select[Prime[Range[2,3000]],Prime[PrimePi[ # ]-1]+Prime[PrimePi[ # ]+1]+Prime[PrimePi[ # ]+2]==3#&] (* _Zak Seidov_, Aug 04 2006 *)
%o A094933 (Magma)
%o A094933 [NthPrime(n):n in [2..3000]|NthPrime(n-1)+NthPrime(n+1)+NthPrime(n+2)- 3*NthPrime(n) eq 0]; // _Marius A. Burtea_, May 06 2019
%o A094933 (MATLAB)
%o A094933 p=primes(30000);
%o A094933 m=1;
%o A094933 for u=2:length(p)-2
%o A094933   if p(u-1)+p(u+1)+p(u+2)-3*p(u)==0;
%o A094933      sol(m)=p(u);  m=m+1;
%o A094933   end
%o A094933 end
%o A094933 sol % _Marius A. Burtea_, May 06 2019
%Y A094933 Cf. A119381.
%K A094933 easy,nonn
%O A094933 1,1
%A A094933 _Roger L. Bagula_, Jun 17 2004
%E A094933 More terms from _Zak Seidov_, Aug 04 2006
%E A094933 Edited by _N. J. A. Sloane_, Aug 08 2008