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Search: id:A122869
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| 11, 19, 31, 59, 71, 79, 131, 139, 151, 179, 191, 199, 211, 239, 251, 271, 311, 331, 359, 379, 419, 431, 439, 479, 491, 499, 571, 599, 619, 631, 659, 691, 719, 739, 751, 811, 839, 859, 911, 919, 971, 991, 1019, 1031, 1039, 1051, 1091, 1151, 1171, 1231, 1259
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Lucas numbers A000032[n] = Fibonacci[n-1] + Fibonacci[n+1] = A000045[n-1] + A000045[n+1]. a(n) is a subset of A002145[n] Primes of form 4n+3, or Primes which are also Gaussian primes. A002145[n] is a union of a(n) and A122870[n] Primes p that divide Lucas[(p+1)/2]. Final digit of a(n) is 1 or 9, or Mod[a(n),10] = {1,9}. a(n) is a subset of A040105[n] x^4 = 5 has a solution mod p. a(n) is a subset of A040147.
a(n) is a subset of A053032[n] Odd primes p with one zero in Fibonacci numbers mod p or odd primes that divide Lucas numbers of odd index. a(n) is a subset of A064739[n] Primes p such that Fibonacci(p)-1 is divisible by p. a(n) is a subset of A003626[n] Inert rational primes in Q(sqrt(-5)). a(n) is a subset of A076518[n] Numbers n such that Fibonacci(n) == sigma(n) (mod n).
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics. Lucas Number.
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics. Gaussian Prime.
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MATHEMATICA
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Select[Prime[Range[1000]], IntegerQ[(Fibonacci[(#1-1)/2-1]+Fibonacci[(#1-1)/2+1])/#1]&]
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CROSSREFS
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Cf. A000032, A000045, A122870, A002145, A040105, A053032, A064739, A003626, A076518.
Adjacent sequences: A122866 A122867 A122868 this_sequence A122870 A122871 A122872
Sequence in context: A080821 A094517 A049719 this_sequence A106535 A052368 A117873
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KEYWORD
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nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), Sep 16 2006
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