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A180367 Lucas(prime(n+1)) - prime(Lucas(n)), for Lucas numbers beginning at 2. 1
0, 2, 6, 22, 182, 490, 3510, 9240, 63868, 1149468, 3009672, 54017304, 370246314, 969319296, 6643832358, 119218840092, 2139295466336, 5600748260454, 100501350226466, 688846502491240, 1803423556642478, 32361122671978600, 221806434537503870, 3980154972736116440 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Commutator of Primes and Lucas numbers. Some subtlety in indexing -- should we start with 0th Lucas number is 2, and 0th prime is 1? As shown here, I use "first" to mean the initial value as shown in P(n) and L(n), even though their indexing differs. This is to A093062 Fibonacci(prime(i))-prime(Fibonacci(i)) as Fibonacci is to Lucas.

LINKS

Table of n, a(n) for n=0..23.

FORMULA

a(n) = L(prime(n+1)) - prime(L(n)) = A000032(A000040(n+1)) - A000040(A000032(n)) = A180363(n+1) - A094894(n).

EXAMPLE

a(0) = 0 because the 1st prime is 2, and the third Lucas number is A000032(2) = 3; while the 1st Lucas number is 2, and the 2nd prime is 3; with 3-3=0.

a(1) = 2 because the 2nd prime is 3, and A000032(3) = 4; while the 2nd Lucas number is 1, and the first2 prime is 2; with 4-2=2.

a(2) = 6 because the 3rd prime is 5, and the 6th Lucas number (counting "2" as first) is A000032(5) = 11; while the 3rd Lucas number is 3, and the 3rd prime is 5; with 11-5=6.

a(3) = 29 - 7 = 22. a(4) = 199 - 17 = 182.

MAPLE

A000032 := proc(n) option remember; if n <= 1 then op(n+1, [2, 1]) ; else procname(n-1)+procname(n-2) ; end if; end proc:

A094894 := proc(n) ithprime(A000032(n)) ; end proc:

A180363 := proc(n) A000032(ithprime(n)) ; end proc:

A180367 := proc(n) A180363(n+1)-A094894(n) ; end proc: seq(A180367(n), n=0..25) ; # R. J. Mathar, Sep 01 2010

CROSSREFS

Cf. A000032, A000040, A094894, A180363, A093062.

Sequence in context: A171339 A032266 A095856 * A111061 A060803 A213134

Adjacent sequences:  A180364 A180365 A180366 * A180368 A180369 A180370

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Aug 31 2010

EXTENSIONS

Some indices corrected, 3 values corrected, formulas signs swapped - R. J. Mathar, Sep 01 2010

STATUS

approved

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Last modified March 28 20:44 EDT 2020. Contains 333103 sequences. (Running on oeis4.)