A066889 a(n) = g(P(n)+2) - P(n), where P(n) = Product_{k=1..n} Fibonacci(k) and g(i) is the smallest prime >= i.

2, 2, 3, 5, 7, 11, 17, 17, 37, 23, 47, 37, 29, 19, 47, 59, 19, 37, 71, 59, 31, 67, 239, 101, 739, 409, 43, 367, 167, 251, 73, 71, 419, 1567, 107, 83, 223, 191, 227, 449, 97, 173, 103, 523, 79, 137, 223, 1163, 661, 103, 103, 541, 227, 2383, 433, 71

Offset: 1

Author

Frank Buss (fb(AT)frank-buss.de), Jan 22 2002

Keywords

• nonn

Comments

The first 169 terms are primes. Are all terms primes? See links for similar sequences.

Note that g is not the usual "nextprime" function. If the usual nextprime function is used, we get A286296.

Examples

			a(4) = 5 because Fibonacci(1)*Fibonacci(2)*Fibonacci(3)*Fibonacci(4) = 1*1*2*3 = 6, g(6+2) = 11, and 11 - 6 = 5.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..169
• Frank Buss, Prime Puzzles - Frank Buss's Conjecture
• Frank Buss, The B(n) function

Crossrefs

Cf. A000045, A067362, A286296 (the same except for the first two terms).

Programs

Mathematica

Join[{2,2},Drop[NextPrime[#+2]-#&/@FoldList[Times,Fibonacci[ Range[ 60]]],2]] (* Harvey P. Dale, May 31 2017 *)

MuPAD

f := 1:for n from 1 to 100 do f := f*numlib::fibonacci(n):a := nextprime(f+2)-f:print(a) end_for

PARI

{ m=1; for (n=1, 1000, m*=fibonacci(n); write("b066889.txt", n, " ", nextprime(m+2) - m) ) } \\ Harry J. Smith, Apr 05 2010

Extensions

Definition and example corrected by Harvey P. Dale and N. J. A. Sloane, May 31 2017