A191375 - OEIS

A191375

Primes that are the sum of squares of three positive Fibonacci numbers.

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Table of n, a(n) for n=1..45.

FORMULA

a(n) > exp(n^(1/3)*log(phi+1))/5. - Charles R Greathouse IV, Feb 24 2023

EXAMPLE

43 = fib(3)^2 + fib(3)^2 + fib(5)^2 is prime.

MATHEMATICA

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 *)

PROG

(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

CROSSREFS

Cf. A000045, A179459.

Sequence in context: A369171 A309581 A291277 * A260793 A057179 A322962

Adjacent sequences: A191372 A191373 A191374 * A191376 A191377 A191378

KEYWORD

nonn,easy

AUTHOR

Carmine Suriano, Jun 01 2011

STATUS

approved

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