A102859 - OEIS

%I #24 Nov 19 2022 00:53:45

%S 0,1,2,3,10,11,12,13,20,21,22,26,30,31,33,99,100,101,102,103,110,111,

%T 112,113,120,121,122,130,200,201,202,210,211,212,220,221,260,264,300,

%U 301,307,310,311,330,836,990,1000,1001,1002,1003,1010,1011,1012,1013,1020

%N Numbers that when squared and written backwards give a square again.

%C Contains A002778. - _Robert Israel_, Sep 20 2015

%C Squares of these terms are in A061457. - _Jon E. Schoenfield_, May 17 2022

%H Jon E. Schoenfield, <a href="/A102859/b102859.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Sq#sqrev">Index entry for sequences related to reversing digits of squares</a>

%F a(n) = sqrt(A061457(n)). - _Jon E. Schoenfield_, May 17 2022

%e a(7)=12 belongs to the sequence since writing 12^2 = 144 backwards gives 441 = 21^2.

%p rev:= proc(n)

%p   local L, Ln, i;

%p   L:= convert(n, base, 10);

%p   Ln:= nops(L);

%p   add(L[i]*10^(Ln-i), i=1..Ln);

%p end proc:

%p select(t -> issqr(rev(t^2)),[$0..10^5]); # _Robert Israel_, Sep 20 2015

%t Select[Range[1000], IntegerQ[Sqrt[FromDigits[Reverse[IntegerDigits[ #^2]]]]] &]

%o (Magma) [n: n in [0..1100] | IsSquare(Seqint(Reverse(Intseq(n^2))))]; // _Vincenzo Librandi_, Sep 21 2015

%o (Python)

%o from itertools import count, islice

%o from sympy import integer_nthroot

%o def A102859_gen(startvalue=0): # generator of terms >= startvalue

%o     return filter(lambda n:integer_nthroot(int(str(n**2)[::-1]),2)[1], count(max(startvalue,0)))

%o A102859_list = list(islice(A102859_gen(),30)) # _Chai Wah Wu_, Nov 18 2022

%Y Cf. A002778, A002942.

%Y Cf. A061457 (squares).

%K base,easy,nonn

%O 1,3

%A Sanita Kashcheyeva (sanits(AT)gmail.com), Mar 01 2005

%E 0 inserted by _Jon E. Schoenfield_, Sep 20 2015