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A218386 A215929(n) - (-1)^Fibonacci(n+1)*A218086(n). 1
2, 5, 19, 257, 196687 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Where {c} constitutes the positive solutions to the short proof of the Crystallographic Restriction Theorem = {1, 2, 3, 4, 6} (see A217290), prime(c) are the Frampton-Kephart primes = {2, 3, 5, 7, 13} (see A217396) and Lambda_c is the c-th laminated lattice Kissing number = {2, 6, 12, 24, 72} (see A002336), let y = (prime(c) - totient(c)) = partition(c) = (Lambda_c - c)/c = {1, 2, 3, 5, 11}. Then, Prime(Fibonacci(2y)) gives this sequence (see A030427).

LINKS

Table of n, a(n) for n=0..4.

FORMULA

(2^|c-2| + 2(c-2))*(2^Fibonacci(c+1) - 2) - (-1)^Fibonacci(n+1)*A218086, where c = {1, 2, 3, 4, 6}, Fibonacci(c + 1) = {1, 2, 3, 5, 13} and Fibonacci(n+1) = {1, 1, 2, 3, 5}

EXAMPLE

0 - 2(-1)^1 = 2, the 1st prime.

2 - 3(-1)^1  = 5, the 3rd prime.

24 - 5(-1)^2  = 19, the 8th prime.

240 - 17(-1)^3  = 257, the 55th prime.

196560 - 127(-1)^5  = 196687, the 17711th prime.

{1, 3, 8, 55, 17711} are all Fibonacci numbers.

CROSSREFS

Cf. A215929, A218086.

Sequence in context: A202422 A212269 A080280 * A055813 A119550 A119563

Adjacent sequences:  A218383 A218384 A218385 * A218387 A218388 A218389

KEYWORD

nonn

AUTHOR

Raphie Frank, Oct 27 2012

STATUS

approved

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Last modified April 18 16:52 EDT 2019. Contains 322216 sequences. (Running on oeis4.)