A100700 -id:A100700 - cp's OEIS frontend

A004397 a(n) = prime(n) + Fibonacci(n).

3, 4, 7, 10, 16, 21, 30, 40, 57, 84, 120, 181, 274, 420, 657, 1040, 1656, 2645, 4248, 6836, 11019, 17790, 28740, 46457, 75122, 121494, 196521, 317918, 514338, 832153, 1346396, 2178440, 3524715, 5703026, 9227614, 14930503, 24157974, 39088332, 63246153

Offset: 1

Hegermann, Frank (hegermann(AT)oi.dbv.commerzbank.dbp.de)

nonn

GCHQ, The GCHQ Puzzle Book, Penguin, 2016. See page 79.

Cf. A100700.

[NthPrime(n)+Fibonacci(n): n in [1..50]]; // Vincenzo Librandi, Jul 29 2016

with(combinat): f := n -> fibonacci(n) + ithprime(n);

Mathematica
```
Table[Fibonacci[n] + Prime[n], {n, 35}]
```

A102867 Prime differences between k-th prime and k-th Fibonacci number.

Original entry on oeis.org

-2, -3, -5, 2, 11, 107, 563, 46279, 3524441, 4807526753, 47068900554068939361891195233676009091941689423

Offset: 1

Jonathan Vos Post, Mar 01 2005

Note that for k>3, F(k) - Prime(k) cannot be prime if k is prime.

The next term -- a(11) -- has 110 digits. - Harvey P. Dale, Mar 19 2017

			F(2)-Prime(2) = 1 - 3 = -2.
F(3)-Prime(3) = 2 - 5 = -3.
F(6)-Prime(6) = 8 - 13 = -5.
F(8)-Prime(8) = 21 - 19 = 2.
F(9)-Prime(9) = 34 - 23 = 11.
F(12)-Prime(12) = 144 - 37 = 107.
F(15)-Prime(15) = 610 - 47 = 563.
F(24)-Prime(24) = 46368 - 89 = 46279.
F(33)-Prime(33) = 3524578 - 137 = 3524441.

Cf. A000040, A000045, A100700.

With[{nn=600},Select[#[[1]]-#[[2]]&/@Thread[{Fibonacci[Range[nn]], Prime[ Range[ nn]]}],PrimeQ]] (* Harvey P. Dale, Mar 19 2017 *)

Fibonacci(k) - Prime(k) iff prime. Intersection of {A000045(i) - A000040(i)} and {A000040(j)}. Prime values of A100700.

More terms from Harvey P. Dale, Mar 19 2017

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A004397 a(n) = prime(n) + Fibonacci(n).

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A102867 Prime differences between k-th prime and k-th Fibonacci number.

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