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A359173 Numbers whose square can be expressed as k * A004086(k) with non-palindromic k.

%I A359173 #17 Dec 23 2022 11:21:27
%S A359173 10,20,30,40,50,60,70,80,90,100,110,200,220,252,300,330,400,403,440,
%T A359173 500,504,550,600,660,700,770,800,816,880,900,990,1000,1010,1100,1110,
%U A359173 1210,1310,1410,1510,1610,1710,1810,1910,2000,2020,2120,2200,2220,2320,2420,2520,2620,2720,2772
%N A359173 Numbers whose square can be expressed as k * A004086(k) with non-palindromic k.
%C A359173 If k is a term, then so is 10*k. - _Robert Israel_, Dec 23 2022
%H A359173 Robert Israel, <a href="/A359173/b359173.txt">Table of n, a(n) for n = 1..2000</a>
%e A359173 a(1) = 10 because 100*1 = 10^2;
%e A359173 a(2) = 20: 200*2 = 20^2;
%e A359173 a(11) = 110: 1100*11 = 110^2;
%e A359173 a(14) = 252: 144*441 = 252^2;
%e A359173 a(28) = 816: 768*867 = 816^2.
%p A359173 rev:= proc(n) local L,i; L:= convert(n,base,10); add(L[-i]*10^(i-1),i=1..nops(L)) end proc:
%p A359173 g:= proc(d,m) local r; r:= rev(d); r <> d and m = d*r end proc:
%p A359173 filter:= proc(n) ormap(g, numtheory:-divisors(n^2),n^2) end proc:
%p A359173 select(filter, [$1..3000]); # _Robert Israel_, Dec 23 2022
%o A359173 (PARI) L=List(); for (k=1, 3*10^6, my (r=fromdigits(Vecrev(digits(k))), s); if (issquare(r*k, &s) && r!=k, if(s<3001, listput(L, s)))); Set(L)
%o A359173 (Python)
%o A359173 from itertools import count, islice
%o A359173 from sympy import divisors
%o A359173 def A359173_gen(startvalue=1): # generator of terms >= startvalue
%o A359173     return filter(lambda n:any(d*int(str(d)[::-1])==n**2 for d in divisors(n**2,generator=True) if d != n),count(max(startvalue,1)))
%o A359173 A359173_list = list(islice(A359173_gen(),30)) # _Chai Wah Wu_, Dec 19 2022
%Y A359173 Cf. A000290, A002113, A004086, A118959.
%K A359173 nonn,base
%O A359173 1,1
%A A359173 _Hugo Pfoertner_, Dec 17 2022