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

1, 3, 5, 7, 10, 11, 14, 15, 19, 21, 23, 30, 33, 34, 37, 41, 42, 43, 46, 51, 55, 58, 59, 61, 67, 69, 70, 73, 77, 78, 82, 85, 86, 87, 89, 91, 94, 95, 101, 102, 105, 106, 109, 111, 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

Offset

1,2

Comments

This is to squarefree numbers what A061783 is to primes.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

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

Maple

R:= n-> (s-> parse(cat(s[-i]$i=1..length(s))))(""||n):
q:= n-> andmap(numtheory[issqrfree], [n, n+R(n)]):
select(q, [$1..200])[];  # Alois P. Heinz, Jan 07 2022

Mathematica

okQ[n_] := SquareFreeQ[n] && SquareFreeQ[n + IntegerReverse[n]];
Select[Range[200], okQ]

Prog

(PARI) isok(m) = issquarefree(m) && issquarefree(m+fromdigits(Vecrev(digits(m)))); \\ Michel Marcus, Jan 07 2022
(Python)
from sympy.ntheory.factor_ import core
def squarefree(n): return core(n, 2) == n
def ok(n): return squarefree(n) and squarefree(n + int(str(n)[::-1]))
print([k for k in range(1, 200) if ok(k)]) # Michael S. Branicky, Jan 07 2022

Crossrefs

Cf. A004086, A005117, A056964, A061783.

Sequence in context: A189171 A189220 A189009 * A206812 A189372 A108052

Adjacent sequences: A350572 A350573 A350574 * A350576 A350577 A350578

Keyword

nonn,base,easy

Author

Jean-François Alcover, Jan 07 2022

Status

approved