OFFSET
1,1
LINKS
Michael S. Branicky, Table of n, a(n) for n = 1..1031 (all terms <= 40 digits)
David A. Corneth, PARI program
EXAMPLE
522729 is in the sequence since reversed the left half is the square 15^2 and the right half is the square 27^2.
A 6-digit term might start with 522 as 522 is the reversal of a three-digit square (namely 225 = 15^2). If a 6-digit term starts with 522 then it is between (inclusive) 522100 and 522999. The only such square is 522729. As 729 (= 522729 - 522000) is a square we have 522729 is in the sequence. - David A. Corneth, Nov 21 2023
PROG
(Python)
from math import isqrt
from itertools import count, islice
def agen(): # generator of terms
for k in count(1):
lb, ub, sk = isqrt(10**(k-1)-1)+1, isqrt(10**k-1), set()
for i in range(lb, ub+1):
if i%10 == 0: continue
left = int(str(i*i)[::-1]) * 10**k
# loop below based on idea by David A. Corneth in Example
lbt, ubt = isqrt(left-1)+1, isqrt(left + 10**k - 1)
for t in range(lbt, ubt+1):
tt = t*t
right = tt - left
sr = str(right)
if len(sr) == k and isqrt(right)**2 == right:
sk.add(tt)
found += len(sk)
yield from sorted(sk)
print(list(islice(agen(), 20))) # Michael S. Branicky, Nov 21 2023
(PARI) \\ See PARI link
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Reiner Moewald, Nov 15 2023
EXTENSIONS
More terms from David A. Corneth, Nov 20 2023
STATUS
approved