OFFSET
1,1
COMMENTS
1 = Fibonacci(1) = Fibonacci(2), so cases where the Fibonacci number is 1 are counted as two ways. Also, if Fibonacci(i) and Fibonacci(j) are both primes (with i <> j), Fibonacci(i) + Fibonacci(j) and Fibonacci(j) + Fibonacci(i) are counted as two ways. - Robert Israel, Aug 22 2024
REFERENCES
J. Earls, "Fibonacci Prime Decompositions," Mathematical Bliss, Pleroma Publications, 2009, pages 76-79. ASIN: B002ACVZ6O
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
In the decomposition of 1081, the prime and Fibonacci both have three digits: 1081 = 144 + 937.
MAPLE
filter:= proc(n) local f, i, d, state;
state:= 0;
for i from 0 do
f:= combinat:-fibonacci(i);
if f >= n then return (state = 1) fi;
if isprime(n-f) then
state:= state+1;
if state = 2 then return false fi;
if f = 0 then d:= 1 else d:= 1+ilog10(f) fi;
if 1+ilog10(n-f) <> d then return false fi;
fi
od;
end proc:
select(filter, [$1..2000]); # Robert Israel, Aug 22 2024
CROSSREFS
KEYWORD
base,easy,nonn
AUTHOR
Jason Earls, Nov 24 2009
EXTENSIONS
Definition clarified by Robert Israel, Aug 22 2024
STATUS
approved