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A362409
a(n) is the least number that is the sum of a Fibonacci number and a square in exactly n ways.
2
15, 7, 3, 1, 17
OFFSET
0,1
COMMENTS
a(n) is the least k such that there are n pairs (i,j) of nonnegative integers such that A000045(i) + j^2 = k.
We count A000045(1) and A000045(2) separately, even though both are 1.
a(5) > 10^20, if it exists. - Martin Ehrenstein, May 01 2023
EXAMPLE
a(0) = 15 because 15 is not the sum of a Fibonacci number and a square.
a(1) = 7 because 7 = A000045(4) + 2^2 is the sum of a Fibonacci number and a square in one way.
a(2) = 3 because 3 = A000045(3) + 1^2 = A000045(4) + 0^2.
a(3) = 1 because 1 = A000045(0) + 1^2 = A000045(1) + 0^2 = A000045(2) + 0^2.
a(4) = 17 because 17 = A000045(1) + 4^2 = A000045(2) + 4^2 = A000045(6) + 3^2 = A000045(7) + 2^2.
MAPLE
N:= 10^8: # to get terms <= N
V:= Array(0..N):
for i from 0 do
f:= combinat:-fibonacci(i);
if f >= N then break fi;
s:= floor(sqrt(N-f));
J:=[seq(f+i^2, i=0..s)];
V[J]:= V[J] +~ 1;
od:
W:= Array(0..max(V)):
for i from 1 to N do
w:= V[i];
if W[w] = 0 then W[w]:= i fi
od:
convert(W, list);
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Robert Israel, Apr 21 2023
STATUS
approved