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 A214434 Composite numbers k such that k divides Fibonacci(k+1) or Fibonacci(k-1) and 2^(k-1) == 1 (mod k). 1
 6601, 13981, 30889, 68101, 219781, 252601, 332949, 399001, 512461, 642001, 721801, 722261, 741751, 852841, 873181, 1024651, 1141141, 1193221, 1207361, 1533601, 1690501, 1735841, 1857241, 1909001, 2085301, 2100901, 2165801, 2603381, 2704801, 2757241, 3186821, 3568661 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Pseudoprimes to a criterion for primality which tests that 1. k divides Fibonacci(k+1) or Fibonacci(k-1) (see A182554, A081264), and 2. 2^(k-1) == 1 (mod k) (see A001567). All terms appear to be congruent to 1 or -1 (mod 5). Terms that are not congruent to 1 or -1 (mod 5): 22711873, 40160737, 55462177, ... . - Amiram Eldar, Sep 12 2022 LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..671 from Giovanni Resta) FORMULA Intersection of A182554 and A001567. EXAMPLE 6601 is in the sequence because the 6600th Fibonacci number is divisible by 6601 and 2^6600 = 1 mod 6601. MAPLE with(combinat):f:= n-> fibonacci(n): for n from 1 to 2000000 do if(f(n+1) mod n = 0 or f(n-1) mod n = 0) and 2^(n-1) mod n = 1 and not isprime(n) then print(n) fi od; MATHEMATICA Select[Range[1, 4*10^6, 2], CompositeQ[#] && PowerMod[2, # - 1, #] == 1 && (Divisible[Fibonacci[# - 1], #] || Divisible[Fibonacci[# + 1], #]) &] (* Amiram Eldar, Sep 12 2022 *) CROSSREFS Cf. A182554, A081264, A001567. Sequence in context: A186563 A252637 A164971 * A317247 A290281 A178213 Adjacent sequences: A214431 A214432 A214433 * A214435 A214436 A214437 KEYWORD nonn AUTHOR Gary Detlefs, Jul 17 2012 STATUS approved

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Last modified March 22 22:02 EDT 2023. Contains 361434 sequences. (Running on oeis4.)