A391727 Numbers k such that A115873(k) is not a binary palindrome (in A006995).

203, 333, 405, 406, 471, 666, 681, 809, 810, 812, 923, 939, 942, 1209, 1332, 1357, 1362, 1457, 1461, 1465, 1617, 1618, 1620, 1624, 1633, 1659, 1683, 1811, 1846, 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

Offset

1,1

Comments

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

Links

Antti Karttunen, Table of n, a(n) for n = 1..3198 (terms less than 2^18)

Index entries for sequences defined by congruent products between domains N and GF(2)[X]

Index entries for sequences related to binary expansion of n.

Index entries for sequences related to carryless arithmetic.

Formula

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

Prog

(PARI)
is_A006995(n) =  (Vecrev(n=binary(n)) == n);
A006068(n) = { my(s=1, ns); while(1, ns = n >> s; if(0==ns, return(n)); n = bitxor(n, ns); s <<= 1); };
A048720(b, c) = fromdigits(Vec(Pol(binary(b))*Pol(binary(c)))%2, 2);
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)));
is_A391727(n) = !is_A006995(A115873(n));

Crossrefs

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

Subsequence of A391730.

Sequence in context: A090486 A348664 A228320 * A346899 A247921 A346883

Adjacent sequences: A391724 A391725 A391726 * A391728 A391729 A391730

Keyword

nonn,base

Author

Antti Karttunen, Dec 20 2025

Status

approved