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

1,2

Links

Table of n, a(n) for n=1..56.

Index entries for sequences related to binary expansion of n

Index entries for sequences operating on polynomials in ring GF(2)[X]

Formula

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

Prog

(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)));

Crossrefs

Odd bisection of A379126.

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

Sequence in context: A265377 A379237 A187554 * A338010 A267702 A339995

Adjacent sequences: A379125 A379126 A379127 * A379129 A379130 A379131

Keyword

nonn

Author

Antti Karttunen, Dec 21 2024

Status

approved