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

Offset: 1

Author

Jonathan Vos Post, Aug 31 2010

Keywords

• easy
• nonn

Comments

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

Examples

			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.
		

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.

Crossrefs

Cf. A000032, A000040, A000045, A030426.

Programs

Magma

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

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 *)

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

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

Extensions

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

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