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A244801
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Smallest m such that for the prime p = prime(n) the congruence F_(p-(p/5)) == mp (mod p^2) holds (i.e., smallest m such that prime(n) is a near-Wall-Sun-Sun prime), where F_k is the k-th Fibonacci number and (p/5) is the Legendre symbol.
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10
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1, 1, 1, 3, 5, 3, 16, 3, 15, 26, 25, 13, 39, 39, 16, 28, 10, 48, 7, 55, 58, 49, 21, 5, 37, 97, 22, 24, 26, 60, 13, 64, 58, 117, 120, 60, 44, 160, 44, 130, 174, 131, 94, 31, 141, 5, 112, 3, 154, 18, 29, 5, 182, 250, 2, 105
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OFFSET
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1,4
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COMMENTS
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A value of 0 indicates a Wall-Sun-Sun prime. No such prime is known and if one exists it is > 4*10^16 (cf. PrimeGrid WSS statistics).
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LINKS
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MATHEMATICA
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A= 0; p = 0; While[A < 200, p = NextPrime[p]; A= Mod[(Fibonacci[p-JacobiSymbol[p, 5]])/p, p]; Print[A]] (* Javier Rivera Romeu, Jan 11 2022 *)
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PROG
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(PARI) forprime(p=2, 10^2, a=fibonacci(p-kronecker(p, 5))%p^2; a=a/p; print1(a, ", "))
(Sage)
A, p = 0, 0
while A <200:
p = next_prime(p)
A = (fibonacci(p-legendre_symbol(p, 5))/p)%p
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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