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

%I #18 Sep 08 2022 08:45:13

%S 127,149,431,967,1031,1061,1597,2437,2833,2953,3793,5923,6449,6701,

%T 6959,7103,8803,11467,11617,11717,11923,12611,13291,13327,13397,13679,

%U 13721,14533,14713,15787,16087,17417,17921,18539,20021,21269,21467,22027

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

%H Robert Israel, <a href="/A094933/b094933.txt">Table of n, a(n) for n = 1..10000</a>

%e 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 p:= 2: q:= 3: r:= 5: s:= 7:

%p count:= 0: Res:= NULL:

%p while count < 100 do

%p if p + r + s = 3*q then count:= count+1; Res:= Res, q fi;

%p p:= q; q:= r; r:= s; s:= nextprime(s)

%p od:

%p Res; # _Robert Israel_, May 06 2019

%t 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 Select[Prime[Range[2,3000]],Prime[PrimePi[ # ]-1]+Prime[PrimePi[ # ]+1]+Prime[PrimePi[ # ]+2]==3#&] (* _Zak Seidov_, Aug 04 2006 *)

%o (Magma)

%o [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 (MATLAB)

%o p=primes(30000);

%o m=1;

%o for u=2:length(p)-2

%o if p(u-1)+p(u+1)+p(u+2)-3*p(u)==0;

%o sol(m)=p(u); m=m+1;

%o end

%o end

%o sol % _Marius A. Burtea_, May 06 2019

%Y Cf. A119381.

%K easy,nonn

%O 1,1

%A _Roger L. Bagula_, Jun 17 2004

%E More terms from _Zak Seidov_, Aug 04 2006

%E Edited by _N. J. A. Sloane_, Aug 08 2008