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

1,2

Comments

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

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

Example

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

Mathematica

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

Prog

(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
(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

Crossrefs

Subsequence of A115690.

Cf. A007488, A007500, A061457, A354256.

Sequence in context: A042381 A230743 A367075 * A156317 A115676 A115667

Adjacent sequences: A033291 A033292 A033293 * A033295 A033296 A033297

Keyword

base,nonn

Author

Jeff Burch

Extensions

More terms from Erich Friedman

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

Status

approved