A379128 a(1) = 1; for n > 1, a(n) is the least odd number k such that A325567(k) = 2*n-1, or 0 if no such number exists.

1, 9, 35, 49, 135, 33, 65, 225, 527, 133, 651, 161, 775, 837, 899, 961, 2079, 525, 259, 273, 2583, 129, 2835, 705, 3087, 3213, 3339, 385, 1539, 3717, 3843, 3969, 8255, 2077, 1035, 1065, 9271, 2325, 1155, 1185, 4131, 2573, 10795, 2697, 11303, 2821, 11811, 2945, 12319, 12573, 12827, 1545, 13335, 13589, 13843, 1665

Offset: 1

Author

Antti Karttunen, Dec 21 2024

Keywords

• nonn

Links

• Index entries for sequences related to binary expansion of n
• Index entries for sequences operating on polynomials in ring GF(2)[X]

Crossrefs

Odd bisection of A379126.

Cf. A048720, A065621, A277320, A325567, A379127.

Programs

PARI

A048720(b, c) = fromdigits(Vec(Pol(binary(b))*Pol(binary(c)))%2, 2);
A065621(n) = bitxor(n-1, n+n-1);
A325567(n) = if(1==n, n, fordiv(n, d, if((d>1)&&A048720(A065621(n/d), d)==n, return(n/d))));
memoA379127 = Map();
A379127(n) = if(1==n,1,my(v); if(mapisdefined(memoA379127,n,&v), v, v = A325567(2*n-1); mapput(memoA379127,n,v); (v)));
A379128(n) = for(k=1,oo,if(A379127(k)==(n+n-1), return(k+k-1)));

Formula

a(n) = A379126(2*n-1).