login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A322005
Least prime p such that n + p is a Fibonacci number (A000045).
2
2, 2, 3, 2, 17, 3, 2, 137, 5, 601, 3, 2, 43, 131, 7, 19, 5, 17, 3, 2, 967, 13, 67, 11, 31, 927372692193078999151, 29, 7, 61, 5, 59, 3, 2, 577, 199, 109, 19, 107, 17, 571, 193, 103, 13, 101, 11, 2539, 43, 97, 7, 14930303, 5, 27777890035237, 3, 2, 179, 89, 6709, 10889, 31, 46309, 29, 83, 6703, 547, 313, 79, 23, 46301, 919, 541, 19, 73, 17
OFFSET
0,1
COMMENTS
See A322004 for the indices of the corresponding Fibonacci numbers, and further information.
LINKS
EXAMPLE
a(0) = 2 is the smallest prime p such that p + 0 (= 2) is a Fibonacci number.
a(1) = 2 is the smallest prime p such that p + 1 (= 3) is a Fibonacci number.
a(2) = 3 is the smallest prime p such that p + 2 (= 5) is a Fibonacci number.
MAPLE
f:= proc(n) local p, k, a, b, c;
a:= -n:b:= 1-n:
do
c:= b;
b:= a+b+n;
a:= c;
if isprime(b) then return b fi
od
end proc:
map(f, [$0..80]); # Robert Israel, Dec 14 2018
MATHEMATICA
primeQ[n_] := n>0 && PrimeQ[n]; a[n_] := Module[{i=2}, While[!primeQ[Fibonacci[i] - n], i++]; Fibonacci[i] - n]; Array[a, 27, 0] (* Amiram Eldar, Dec 12 2018 *)
PROG
(PARI) a(n)=for(i=1, oo, ispseudoprime(fibonacci(i)-n)&&return(fibonacci(i)-n))
CROSSREFS
KEYWORD
nonn
AUTHOR
M. F. Hasler, Dec 12 2018
STATUS
approved