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%I #13 Jan 21 2024 09:38:36
%S 1,3,7,5,15,9,31,21,11,13,63,17,51,127,85,33,73,255,27,45,511,65,341,
%T 23,107,29,19,189,195,25,1023,273,69,81,455,129,585,79,93,819,207,121,
%U 243,2047,1365,279,635,443,889,465,4095,257,1419,1677,1057,313,1335
%N Distinct values of A369317, in order of appearance.
%C All terms are even.
%C This sequence is infinite as it contains A126646.
%C Will every odd number appear in the sequence?
%C Empirically, each odd number, say v, appears in A369317, and the first index is of the form v*2^k - 1 for some k > 0 (see Example section).
%H Rémy Sigrist, <a href="/A369277/a369277.gp.txt">PARI program</a>
%H <a href="/index/Ge#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%e The first terms, alongside their index m in A369317, in decimal and in binary, are:
%e n a(n) m bin(a(n)) bin(m)
%e -- ---- ---- --------- ------------
%e 1 1 1 1 1
%e 2 3 5 11 101
%e 3 7 27 111 11011
%e 4 5 39 101 100111
%e 5 15 119 1111 1110111
%e 6 9 287 1001 100011111
%e 7 31 495 11111 111101111
%e 8 21 671 10101 1010011111
%e 9 11 703 1011 1010111111
%e 10 13 831 1101 1100111111
%e 11 63 2015 111111 11111011111
%e 12 17 2175 10001 100001111111
%o (PARI) See Links section.
%Y Cf. A126646, A369317.
%K nonn,base
%O 1,2
%A _Rémy Sigrist_, Jan 20 2024