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

10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 200, 220, 252, 300, 330, 400, 403, 440, 500, 504, 550, 600, 660, 700, 770, 800, 816, 880, 900, 990, 1000, 1010, 1100, 1110, 1210, 1310, 1410, 1510, 1610, 1710, 1810, 1910, 2000, 2020, 2120, 2200, 2220, 2320, 2420, 2520, 2620, 2720, 2772

Offset: 1

Author

Hugo Pfoertner, Dec 17 2022

Keywords

• nonn
• base

Comments

If k is a term, then so is 10*k. - Robert Israel, Dec 23 2022

Examples

			a(1) = 10 because 100*1 = 10^2;
a(2) = 20: 200*2 = 20^2;
a(11) = 110: 1100*11 = 110^2;
a(14) = 252: 144*441 = 252^2;
a(28) = 816: 768*867 = 816^2.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A000290, A002113, A004086, A118959.

Programs

Maple

rev:= proc(n) local L,i; L:= convert(n,base,10); add(L[-i]*10^(i-1),i=1..nops(L)) end proc:
g:= proc(d,m) local r; r:= rev(d); r <> d and m = d*r end proc:
filter:= proc(n) ormap(g, numtheory:-divisors(n^2),n^2) end proc:
select(filter, [$1..3000]); # Robert Israel, Dec 23 2022

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)

Python

from itertools import count, islice
from sympy import divisors
def A359173_gen(startvalue=1): # generator of terms >= startvalue
    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)))
A359173_list = list(islice(A359173_gen(),30)) # Chai Wah Wu, Dec 19 2022