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A375643
Numbers that are the sum of a prime and a Fibonacci number in exactly one way.
2
2, 9, 17, 27, 29, 33, 59, 65, 70, 77, 83, 85, 89, 90, 93, 95, 99, 121, 123, 124, 127, 129, 133, 143, 145, 146, 153, 155, 166, 169, 174, 179, 188, 189, 190, 195, 203, 210, 217, 219, 222, 237, 239, 243, 249, 258, 261, 267, 269, 289, 297, 302, 303, 305, 308, 309, 310, 321, 323, 327, 331, 333, 335
OFFSET
1,1
COMMENTS
Numbers k such that k - A000045(i) is prime for exactly one i >= 0.
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.
LINKS
EXAMPLE
a(5) = 29 is a term because 29 - Fibonacci(i) is prime only for i = 0.
MAPLE
filter:= proc(n) local f, i, d, state;
state:= 0;
for i from 0 do
if i = 2 then next fi;
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;
fi
od;
end proc:
select(filter, [$1..1000]);
CROSSREFS
Cf. A000045, A132144, A375642. Contains A168383.
Sequence in context: A137189 A028503 A100291 * A126082 A083707 A240651
KEYWORD
nonn
AUTHOR
Robert Israel, Aug 22 2024
STATUS
approved