A391727 - OEIS

%I #12 Dec 21 2025 00:15:41

%S 203,333,405,406,471,666,681,809,810,812,923,939,942,1209,1332,1357,

%T 1362,1457,1461,1465,1617,1618,1620,1624,1633,1659,1683,1811,1846,

%U 1878,1884,1899,1967,1997,2337,2418,2625,2657,2664,2713,2714,2724,2729,2785,2853,2914,2922,2930,3109,3221,3234,3236,3237,3240,3243

%N Numbers k such that A115873(k) is not a binary palindrome (in A006995).

%C If k is a term, then 2*k is also a term, and vice versa.

%H Antti Karttunen, <a href="/A391727/b391727.txt">Table of n, a(n) for n = 1..3198</a> (terms less than 2^18)

%H <a href="/index/Con#CongruCrossDomain">Index entries for sequences defined by congruent products between domains N and GF(2)[X]</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>.

%H <a href="/index/Ca#CARRYLESS">Index entries for sequences related to carryless arithmetic</a>.

%F {k such that A030101(A115873(k)) is not equal to A115873(k)}.

%o (PARI)

%o is_A006995(n) =  (Vecrev(n=binary(n)) == n);

%o A006068(n) = { my(s=1, ns); while(1, ns = n >> s; if(0==ns, return(n)); n = bitxor(n, ns); s <<= 1); };

%o A048720(b, c) = fromdigits(Vec(Pol(binary(b))*Pol(binary(c)))%2, 2);

%o A115873(n) = forstep(k=1,oo,2,my(t=bitxor(k,k*n)); if(!(hammingweight(t)%2) && A006068(t) == 2*A048720(k,n-1), return(k)));

%o is_A391727(n) = !is_A006995(A115873(n));

%Y Cf. A006995, A030101, A154809, A391728 [= A115873(a(n))].

%Y Subsequence of A391730.

%K nonn,base

%O 1,1

%A _Antti Karttunen_, Dec 20 2025