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

1,1

Comments

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

Links

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

Example

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.

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

Prog

(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

Crossrefs

Cf. A000290, A002113, A004086, A118959.

Sequence in context: A263172 A008592 A158814 * A118959 A273239 A343452

Adjacent sequences: A359170 A359171 A359172 * A359174 A359175 A359176

Keyword

nonn,base

Author

Hugo Pfoertner, Dec 17 2022

Status

approved