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A121710
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The smallest prime of the form (prime(n+1)^k + prime(n+2)^k)/2 for positive integer k.
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2
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17, 37, 8521, 21601, 229, 106921, 205081, 289278699121, 815401, 1398841, 8274567108488469403564696641244659777685186165444353190460129729940809291805549571887038803603334751361, 3122281, 2029
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OFFSET
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1,1
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COMMENTS
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These numbers are all of the form 4n+1.
k needs to be a power of two. The sequence of the associated k is 2, 2, 4, 4, 2, 4, 4, 8, 4, 4, 64, 4, 2, 0, 32, 4, 4, 4, 0, 0, 0, 8, 0, 0, 8, 4, 8, 4, 2, 4, 0, 32, 0, 2, 8, 2, ... where 0 is inserted if a(n) does not appear to exist. - Robert G. Wilson v, Aug 02 2018
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LINKS
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MAPLE
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local p1, p2, k, a ;
p1 := ithprime(n+1) ;
p2 := nextprime(p1) ;
for k from 1 do
a := (p1^k+p2^k)/2 ;
if type(a, 'integer') and isprime(a) then
return a;
end if;
end do:
end proc:
for n from 1 do
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PROG
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(PARI) g(n, a, b) = for(x=1, n, y=(a^x+b^x)/2; if(ispseudoprime(y), print(a", "b", "x", "y)))
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CROSSREFS
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KEYWORD
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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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