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

1,1

Links

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

Example

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

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 *)

Prog

(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
(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

Crossrefs

Cf. A119381.

Sequence in context: A164966 A178088 A006285 * A156702 A180536 A342801

Adjacent sequences: A094930 A094931 A094932 * A094934 A094935 A094936

Keyword

easy,nonn

Author

Roger L. Bagula, Jun 17 2004

Extensions

More terms from Zak Seidov, Aug 04 2006

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

Status

approved