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A191375
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Primes that are the sum of squares of three positive Fibonacci numbers.
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0
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3, 11, 17, 19, 43, 59, 137, 179, 347, 443, 449, 467, 491, 509, 569, 619, 883, 907, 1051, 1229, 1601, 2753, 3203, 3467, 3491, 3907, 6491, 8363, 8387, 8803, 20749, 20809, 21893, 24917, 28661, 41641, 44497, 49393, 54323, 55171, 62219, 75029, 108587, 284267, 372173
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OFFSET
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1,1
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LINKS
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FORMULA
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EXAMPLE
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43 = fib(3)^2 + fib(3)^2 + fib(5)^2 is prime.
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MATHEMATICA
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f = Union[Table[Fibonacci[n]^2, {n, 16}]]; t = Union[Flatten[Table[ f[[i]] + f[[j]] + f[[k]], {i, Length[f]}, {j, i, Length[f]}, {k, j, Length[f]}]]]; Select[t, # <= f[[-1]] && PrimeQ[#] &] (* T. D. Noe, Jun 03 2011 *)
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PROG
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(PARI) list(lim)=my(f=List(), v=List()); for(n=1, oo, my(t=fibonacci(n)^2); if(t+2>lim, break); listput(f, t)); for(i=1, #f, for(j=1, i, for(k=1, j, my(p=f[i]+f[j]+f[k]); if(p>lim, break); if(isprime(p), listput(v, p))))); Set(v) \\ Charles R Greathouse IV, Feb 24 2023
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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