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Squarefree numbers k such that k + (k reversed) is also squarefree.
1

%I #18 Jan 11 2022 15:01:35

%S 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 67,69,70,73,77,78,82,85,86,87,89,91,94,95,101,102,105,106,109,111,

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

%C This is to squarefree numbers what A061783 is to primes.

%H Robert Israel, <a href="/A350575/b350575.txt">Table of n, a(n) for n = 1..10000</a>

%e 14 is a term since it's squarefree and so is 14 + 41 = 55.

%p R:= n-> (s-> parse(cat(s[-i]$i=1..length(s))))(""||n):

%p q:= n-> andmap(numtheory[issqrfree], [n, n+R(n)]):

%p select(q, [$1..200])[]; # _Alois P. Heinz_, Jan 07 2022

%t okQ[n_] := SquareFreeQ[n] && SquareFreeQ[n + IntegerReverse[n]];

%t Select[Range[200], okQ]

%o (PARI) isok(m) = issquarefree(m) && issquarefree(m+fromdigits(Vecrev(digits(m)))); \\ _Michel Marcus_, Jan 07 2022

%o (Python)

%o from sympy.ntheory.factor_ import core

%o def squarefree(n): return core(n, 2) == n

%o def ok(n): return squarefree(n) and squarefree(n + int(str(n)[::-1]))

%o print([k for k in range(1, 200) if ok(k)]) # _Michael S. Branicky_, Jan 07 2022

%Y Cf. A004086, A005117, A056964, A061783.

%K nonn,base,easy

%O 1,2

%A _Jean-François Alcover_, Jan 07 2022