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 A345753 Euler-Fibonacci pseudoprimes: odd composites k such that F(k) == 5^((k-1)/2) == +-1 (mod k), where F(k) = A000045(k), the Fibonacci numbers. 0
 146611, 252601, 399001, 512461, 556421, 852841, 1024651, 1193221, 1314631, 1857241, 1909001, 2100901, 2165801, 2603381, 2704801, 3470921, 3828001, 3942271, 4504501, 5049001, 5148001, 5481451, 6189121, 6840001, 7267051, 7519441, 7879681, 8086231, 8341201, 8719921, 9439201, 9863461 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS If p is an odd prime except 5, then F(p) == 5^((p-1)/2) == +-1 (mod p). All terms found satisfy the congruence F(k) == 5^((k-1)/2) == 1 (mod k). They are a proper subset of A094394. Are there odd composites m such that F(m) == 5^((m-1)/2) == -1 (mod m)? They are a proper subset (maybe empty) of A094395 (they are not in the database, below 4*10^9). LINKS Table of n, a(n) for n=1..32. MATHEMATICA Select[Range[1, 10^6, 2], CompositeQ[#] && MemberQ[{1, # - 1}, PowerMod[5, (# - 1)/2, #]] && Divisible[5^((# - 1)/2) - Fibonacci[#], #] &] CROSSREFS Cf. A000045, A094394, A094395, A262052. Sequence in context: A233915 A237297 A204527 * A110084 A224587 A004670 Adjacent sequences: A345750 A345751 A345752 * A345754 A345755 A345756 KEYWORD nonn AUTHOR Amiram Eldar and Thomas Ordowski, Jun 26 2021 STATUS approved

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Last modified December 8 17:58 EST 2023. Contains 367680 sequences. (Running on oeis4.)