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A094933
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Primes prime(k) such that (prime(k-1) + prime(k+1) + prime(k+2))/prime(k) = 3.
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1
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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
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OFFSET
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1,1
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LINKS
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EXAMPLE
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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
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MAPLE
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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:
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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