A391567 - OEIS

%I #20 Dec 16 2025 11:54:35

%S 1,1,3,1,7,3,7,1,15,7,3,3,5,7,15,1,31,15,3,7,5,3,45,3,31,5,2295,7,31,

%T 15,31,1,63,31,3,15,45,3,5,7,7,5,5,3,5,45,5,3,21,31,17391,5,63,2295,

%U 17391,7,9,31,1079,15,21,31,63,1,127,63,3,31,7,3,7,15,9,45,55269,3,3,5,3,7,21,7,3,5,765,5,11,3

%N If n is a power of 2, then a(n) = 1, otherwise we search for the smallest integer m > n, for which there exists an odd number i <= n^3 such that m*i = A048720(n, i), and return that i as the result of a(n). Here A048720 is carryless base-2 multiplication.

%H Antti Karttunen, <a href="/A391567/b391567.txt">Table of n, a(n) for n = 1..207</a>

%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 For all n >= 1, n * a(n) = A048720(A115857(n), a(n)).

%o (PARI)

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

%o A065621(n) = bitxor(n-1, n+n-1);

%o A209229(n) = (n && !bitand(n,n-1));

%o A391567(n) = if(A209229(n), 1, for(m=n+1,A065621(n),forstep(i=1,n^3,2,if((n*i)==A048720(m,i),return(i)))); (0));

%Y Cf. A048720, A115857 (gives the corresponding number m).

%Y Differs from A115873 at positions given by A391568.

%Y Cf. also A391570, A391572.

%K nonn

%O 1,3

%A _Antti Karttunen_, Dec 15 2025