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A308572
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a(n) = Fibonacci(2*prime(n)).
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1
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3, 8, 55, 377, 17711, 121393, 5702887, 39088169, 1836311903, 591286729879, 4052739537881, 1304969544928657, 61305790721611591, 420196140727489673, 19740274219868223167, 6356306993006846248183, 2046711111473984623691759, 14028366653498915298923761, 4517090495650391871408712937
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OFFSET
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1,1
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COMMENTS
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This sequence is noteworthy in light of the congruence relation shared by a(n) and prime(n). Namely, for n > 2, a(n) == prime(n) (mod 10). That is, the last digit of prime(n) is 'preserved' as the last digit of a(n). See A007652.
As well, extending the notion, one notes that for k == 1 (mod 4), Fibonacci(2^k * prime(n)) == prime(n) (mod 10).
For any prime number p, the Fibonacci number F_(2p) == -(2p/5) (mod p), where -(2p/5) is the Legendre or Jacobi symbol. - Yike Li, Aug 30 2022
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LINKS
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FORMULA
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EXAMPLE
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a(4) = 377, because prime(4) = 7, 2*7 = 14, and Fibonacci(14) is 377.
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MAPLE
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f:= n -> combinat:-fibonacci(2*ithprime(n)):
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PROG
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(PARI) a(n) = fibonacci(2*prime(n)); \\ Michel Marcus, Jun 08 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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