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A216275 Fibonacci + Goldbach: a(1)=6, a(2)=8 and for n>=3, a(n)=g(a(n-1)) + g(a(n-2)), where for m>=3, g(2*m) is the maximal prime p < 2*m such that 2*m - p is prime. 4
6, 8, 8, 10, 12, 14, 18, 24, 32, 48, 72, 110, 174, 274, 438, 704, 1134, 1830, 2952, 4762, 7698, 12450, 20128, 32560, 52660, 85168, 137752, 222844, 360564, 583392, 943902, 1527222, 2471074, 3998274, 6469334, 10467566, 16936850, 27404300, 44341050, 71745324 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Conjecture. lim a(n+1)/a(n)=phi as n goes to infinity (phi=golden ratio).

LINKS

Peter J. C. Moses, Table of n, a(n) for n = 1..1000

FORMULA

For n>=5, a(n) = A216835(n-3) + A216835(n-4).

EXAMPLE

Let n=6. Since a(4) = 10, a(5) = 12 and g(10) = g(12) = 7, then a(6) = 7 + 7 = 14.

MATHEMATICA

a[1] = 6; a[2] = 8; g[n_] := Module[{tmp, k=1}, While[!PrimeQ[n-(tmp=NextPrime[n, -k])], k++]; tmp]; a[n_] := a[n] = g[a[n-1]] + g[a[n-2]]; Table[a[n], {n, 1, 100}]

CROSSREFS

Cf. A000045, A002375, A025019, A216835.

Sequence in context: A316858 A316859 A185200 * A315946 A047876 A315947

Adjacent sequences:  A216272 A216273 A216274 * A216276 A216277 A216278

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, Mar 16 2013

STATUS

approved

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Last modified November 29 03:58 EST 2021. Contains 349416 sequences. (Running on oeis4.)