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A122870 Primes p that divide Lucas[(p+1)/2] = A000032[(p+1)/2]. 5


%S 3,7,23,43,47,67,83,103,107,127,163,167,223,227,263,283,307,347,367,

%T 383,443,463,467,487,503,523,547,563,587,607,643,647,683,727,743,787,

%U 823,827,863,883,887,907,947,967,983,1063,1087,1103,1123,1163,1187,1223

%N Primes p that divide Lucas[(p+1)/2] = A000032[(p+1)/2].

%C a(n) is a subset of A002145[n] Primes of form 4n+3, Primes which are also Gaussian primes. A002145[n] is a union of a(n) and A122869[n] Primes p that divide Lucas[(p-1)/2]. Final digit of a(n) is 3 or 7, or Mod[a(n),10] = {3,7}. a(n) = A106865[n+1] Primes of the form 2x^2-2xy+3y^2, with x and y nonnegative, or a(n) are primes congruent to 3,7 modulo 20; Mod[a(n),20] = {3,7}. a(n) is a subset of A003631[n] Primes congruent to {2, 3} mod 5, or primes p that divide Fibonacci(p+1), or Inert rational primes in Q(sqrt 5). a(n) is a subset of A053027[n] Odd primes p with 2 zeros in Fibonacci numbers mod p; or odd primes that divide Lucas numbers of even index. a(n) is a subset of A049098[n] Primes p such that p+1 is divisible by a square.

%H Vincenzo Librandi, <a href="/A122870/b122870.txt">Table of n, a(n) for n = 1..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LucasNumber.html">Lucas Number</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GaussianPrime.html">Gaussian Prime</a>.

%t Select[Prime[Range[1000]],IntegerQ[(Fibonacci[(#1+1)/2-1]+Fibonacci[(#1+1)/2+1])/#1]&]

%Y Cf. A000032, A000045, A122869, A002145, A106865, A053027, A049098, A003631.

%K nonn

%O 1,1

%A _Alexander Adamchuk_, Sep 16 2006

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Last modified October 17 08:36 EDT 2019. Contains 328107 sequences. (Running on oeis4.)