cp's OEIS Frontend

A350575 Squarefree numbers k such that k + (k reversed) is also squarefree.

%I A350575 #18 Jan 11 2022 15:01:35
%S A350575 1,3,5,7,10,11,14,15,19,21,23,30,33,34,37,41,42,43,46,51,55,58,59,61,
%T A350575 67,69,70,73,77,78,82,85,86,87,89,91,94,95,101,102,105,106,109,111,
%U A350575 115,118,119,130,131,134,138,139,141,142,146,149,151,155,158,159,161,166,170,174,178,181,182,185,190,191,194,195,199
%N A350575 Squarefree numbers k such that k + (k reversed) is also squarefree.
%C A350575 This is to squarefree numbers what A061783 is to primes.
%H A350575 Robert Israel, <a href="/A350575/b350575.txt">Table of n, a(n) for n = 1..10000</a>
%e A350575 14 is a term since it's squarefree and so is 14 + 41 = 55.
%p A350575 R:= n-> (s-> parse(cat(s[-i]$i=1..length(s))))(""||n):
%p A350575 q:= n-> andmap(numtheory[issqrfree], [n, n+R(n)]):
%p A350575 select(q, [$1..200])[];  # _Alois P. Heinz_, Jan 07 2022
%t A350575 okQ[n_] := SquareFreeQ[n] && SquareFreeQ[n + IntegerReverse[n]];
%t A350575 Select[Range[200], okQ]
%o A350575 (PARI) isok(m) = issquarefree(m) && issquarefree(m+fromdigits(Vecrev(digits(m)))); \\ _Michel Marcus_, Jan 07 2022
%o A350575 (Python)
%o A350575 from sympy.ntheory.factor_ import core
%o A350575 def squarefree(n): return core(n, 2) == n
%o A350575 def ok(n): return squarefree(n) and squarefree(n + int(str(n)[::-1]))
%o A350575 print([k for k in range(1, 200) if ok(k)]) # _Michael S. Branicky_, Jan 07 2022
%Y A350575 Cf. A004086, A005117, A056964, A061783.
%K A350575 nonn,base,easy
%O A350575 1,2
%A A350575 _Jean-François Alcover_, Jan 07 2022