OFFSET
1,1
COMMENTS
It seems that an analogous case as A072595 for GF(2)[X]-polynomials is just the squares of GF(2)[X]-polynomials (A000695), thus in that ring, the sequence analogous to this one would be empty.
This sequence happens also to encode in the prime factorization of n a certain subset of the Nim game positions that are second-player win.
LINKS
Antti Karttunen and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 75 terms from Karttunen)
Wikipedia, Nim
EXAMPLE
70 is included, as 70 = 2*5*7, whose binary representations are '10', '101' and '111', which when all are xored (cf. A003987) together, cancel all 1-bits, thus yielding zero.
212585 is included, as 212585 = 5*17*41*61, and when we xor their base-2 representations together:
101
10001
101001
111101
--------
000000
we get only zeros, because in each column (bit-position), there is an even number of 1-bits.
MATHEMATICA
Select[Range[82000], SquareFreeQ[#]&&BitXor@@FactorInteger[#][[All, 1]]==0&] (* Harvey P. Dale, Apr 01 2017 *)
PROG
(Scheme, with Antti Karttunen's IntSeq-library)
(define A235488 (MATCHING-POS 1 1 (lambda (n) (and (not (zero? (A008683 n))) (zero? (A072594 n))))))
(PARI) is(n)=if(n<9, return(0)); my(f=factor(n)); vecmax(f[, 2])==1 && fold(bitxor, f[, 1])==0 \\ Charles R Greathouse IV, Aug 06 2016
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Antti Karttunen, Jan 22 2014
STATUS
approved