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

127, 149, 431, 967, 1031, 1061, 1597, 2437, 2833, 2953, 3793, 5923, 6449, 6701, 6959, 7103, 8803, 11467, 11617, 11717, 11923, 12611, 13291, 13327, 13397, 13679, 13721, 14533, 14713, 15787, 16087, 17417, 17921, 18539, 20021, 21269, 21467, 22027

Offset: 1

Author

Roger L. Bagula, Jun 17 2004

Keywords

• easy
• nonn

Examples

			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
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A119381.

Programs

MATLAB

p=primes(30000);
m=1;
for u=2:length(p)-2
  if p(u-1)+p(u+1)+p(u+2)-3*p(u)==0;
     sol(m)=p(u);  m=m+1;
  end
end
sol % Marius A. Burtea, May 06 2019

Magma

[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

Maple

p:= 2: q:= 3: r:= 5: s:= 7:
count:= 0: Res:= NULL:
while count < 100 do
  if p + r + s = 3*q then count:= count+1; Res:= Res, q fi;
  p:= q; q:= r; r:= s; s:= nextprime(s)
od:
Res; # Robert Israel, May 06 2019

Mathematica

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]
Select[Prime[Range[2,3000]],Prime[PrimePi[ # ]-1]+Prime[PrimePi[ # ]+1]+Prime[PrimePi[ # ]+2]==3#&] (* Zak Seidov, Aug 04 2006 *)

Extensions

More terms from Zak Seidov, Aug 04 2006

Edited by N. J. A. Sloane, Aug 08 2008