A180363 - OEIS

A180363

a(n) = Lucas(prime(n)).

3, 4, 11, 29, 199, 521, 3571, 9349, 64079, 1149851, 3010349, 54018521, 370248451, 969323029, 6643838879, 119218851371, 2139295485799, 5600748293801, 100501350283429, 688846502588399, 1803423556807921, 32361122672259149, 221806434537978679

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OFFSET

1,1

COMMENTS

This is to A030426, Fibonacci(prime(n)), as A000032 (Lucas numbers beginning at 2) is to A000045.

LINKS

Table of n, a(n) for n = 1..650

A. Aksenov, The Newman phenomenon and Lucas sequence, arXiv:1108.5352 [math.NT], 2011. [Gives factorizations of first 88 terms]

Paula Burkhardt et al., Visual properties of generalized Kloosterman sums, arXiv:1505.00018 [math.NT], 2015.

FORMULA

a(n) = A000032(A000040(n)) = Lucas(prime(n)).

a(n) = A032170(A000040(n)) / A064723(n-1) - 1 for n>1. - Flávio V. Fernandes, Dec 30 2021

EXAMPLE

a(1) = 3 because the 1st prime is 2, and the 2nd Lucas number is A000032(2) = 3.

a(2) = 4 because the 2nd prime is 3, and the 3rd Lucas number is A000032(3) = 4.

a(3) = 11 because the 3rd prime is 5, and the 5th Lucas number is A000032(5) = 11.

MAPLE

A180363 := proc(n) A000032(ithprime(n)) ; end proc: seq(A180363(n), n=1..30) ; # R. J. Mathar, Sep 01 2010

# second Maple program:

a:= n-> (<<1|1>, <1|0>>^ithprime(n). <<2, -1>>)[1, 1]:

seq(a(n), n=1..50); # Alois P. Heinz, Jan 03 2022

MATHEMATICA

LucasL[Prime[Range[30]]] (* Vincenzo Librandi, Dec 01 2015 *)

PROG

(Magma) [Lucas(NthPrime(n)): n in [1..30]]; // Vincenzo Librandi, Dec 01 2015

(Python)

from sympy import lucas, prime

def a(n): return lucas(prime(n))

print([a(n) for n in range(1, 24)]) # Michael S. Branicky, Dec 30 2021

CROSSREFS

Cf. A000032, A000040, A000045, A030426.

Sequence in context: A042129 A141723 A268478 * A100845 A019169 A049979

Adjacent sequences: A180360 A180361 A180362 * A180364 A180365 A180366

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Aug 31 2010

EXTENSIONS

Entries checked by R. J. Mathar, Sep 01 2010

Edited by N. J. A. Sloane, Nov 28 2011

STATUS

approved