|
%I #25 May 31 2017 21:25:39
%S 2,2,3,5,7,11,17,17,37,23,47,37,29,19,47,59,19,37,71,59,31,67,239,101,
%T 739,409,43,367,167,251,73,71,419,1567,107,83,223,191,227,449,97,173,
%U 103,523,79,137,223,1163,661,103,103,541,227,2383,433,71
%N 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.
%C The first 169 terms are primes. Are all terms primes? See links for similar sequences.
%C Note that g is not the usual "nextprime" function. If the usual nextprime function is used, we get A286296.
%H Harry J. Smith, <a href="/A066889/b066889.txt">Table of n, a(n) for n = 1..169</a>
%H Frank Buss, <a href="http://www.primepuzzles.net/conjectures/conj_028.htm">Prime Puzzles - Frank Buss's Conjecture</a>
%H Frank Buss, <a href="http://www.primepuzzles.net/conjectures/conj_029.htm">The B(n) function</a>
%e 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.
%t Join[{2,2},Drop[NextPrime[#+2]-#&/@FoldList[Times,Fibonacci[ Range[ 60]]],2]] (* _Harvey P. Dale_, May 31 2017 *)
%o (PARI) { m=1; for (n=1, 1000, m*=fibonacci(n); write("b066889.txt", n, " ", nextprime(m+2) - m) ) } \\ _Harry J. Smith_, Apr 05 2010
%o (MuPAD) f := 1:for n from 1 to 100 do f := f*numlib::fibonacci(n):a := nextprime(f+2)-f:print(a) end_for
%Y Cf. A000045, A067362, A286296 (the same except for the first two terms).
%K nonn
%O 1,1
%A Frank Buss (fb(AT)frank-buss.de), Jan 22 2002
%E Definition and example corrected by _Harvey P. Dale_ and _N. J. A. Sloane_, May 31 2017
|
