A033294 Squares which when written backwards remain square (final 0's excluded).

1, 4, 9, 121, 144, 169, 441, 484, 676, 961, 1089, 9801, 10201, 10404, 10609, 12321, 12544, 12769, 14641, 14884, 40401, 40804, 44521, 44944, 48841, 69696, 90601, 94249, 96721, 698896, 1002001, 1004004, 1006009, 1022121, 1024144, 1026169

Offset: 1

Author

Jeff Burch

Keywords

• base
• nonn

Comments

Of this sequence's first 10000 terms, only nine have an even number of digits; see A354256.

Examples

			144 = 12 * 12 is a term because 441 = 21 * 21.
		

Links

• Jon E. Schoenfield, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Reinhard Zumkeller)
• Index entry for sequences related to reversing digits of squares

Crossrefs

Subsequence of A115690.

Cf. A007488, A007500, A061457, A354256.

Programs

Haskell

a033294 n = a033294_list !! (n-1)
a033294_list = filter chi a000290_list where
  chi m = m `mod` 10 > 0 && head ds `elem` [1,4,5,6,9] &&
          a010052 (foldl (\v d -> 10 * v + d) 0 ds) == 1 where
    ds = unfoldr
         (\x -> if x == 0 then Nothing else Just $ swap $ divMod x 10) m
-- Reinhard Zumkeller, Jan 19 2012

Mathematica

Select[Range[1100]^2,Mod[#,10]!=0&&IntegerQ[Sqrt[FromDigits[Reverse[ IntegerDigits[ #]]]]]&] (* Harvey P. Dale, Oct 28 2013 *)

Python

from math import isqrt
from itertools import count, islice
def sqr(n): return isqrt(n)**2 == n
def agen():
    yield from (k*k for k in count(1) if k%10 and sqr(int(str(k*k)[::-1])))
print(list(islice(agen(), 36))) # Michael S. Branicky, May 21 2022

Extensions

More terms from Erich Friedman

Initial 0 removed and offset changed by Reinhard Zumkeller, Jan 19 2012