OFFSET
1,1
COMMENTS
Leading 0's are not allowed, so the first number concatenated cannot be 0.
Sequence based on a suggestion by ChatGPT.
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..93
EXAMPLE
MAPLE
icat:= proc(n, m) if m = 0 then n*10 else n*10^(1+ilog10(m))+m fi end proc:
for i from 1 while length(combinat:-fibonacci(i))<9 do od:
f8:= [seq(combinat:-fibonacci(n), n=2..i-1)]:
s8:= [seq(i^2, i=1..9999)]:
f0:= [0, op(f8)]: s0:= {0, op(s8)}:
S1:= select(t -> t < 10^9, {seq(seq(icat(a, b), a=f8), b=s0)}):
S2:= select(t -> t < 10^9, {seq(seq(icat(a, b), a=s8), b=f0)}):
sort(convert(S1 intersect S2, list));
PROG
(Python)
from math import isqrt
from itertools import count, islice
from sympy.ntheory.primetest import is_square
from sympy import fibonacci
def A361990_gen(): # generator of terms
for l in count(2):
c = set()
for i in range(1, isqrt(10**(l-1)-1)+1):
i2 = i**2
k = 10**(l-len(str(i2))-1)
for j in count(0):
f = int(fibonacci(j))
if f>=10*k:
break
if (f==0 and k==1) or f>=k:
n = i2*10*k+f
for w in range(1, len(str(n))):
w2 = 10**(w-1)
a, b = divmod(n, w2*10)
if w==1 or b>=w2:
if (is_square(b) and (is_square(r:=5*a**2-4) or is_square(r+8))):
c.add(n)
yield from sorted(c)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Robert Israel, Apr 02 2023
EXTENSIONS
Although this was originally suggested by an AI program, it has been fully checked by the OEIS Editors - N. J. A. Sloane, Oct 19 2023
STATUS
approved