A379126 a(1) = 1; for n > 1, a(n) is the least number k such that A325567(k) = n, or 0 if no such number exists.

1, 4, 9, 8, 35, 18, 49, 16, 135, 70, 33, 36, 65, 98, 225, 32, 527, 270, 133, 140, 651, 66, 161, 72, 775, 130, 837, 196, 899, 450, 961, 64, 2079, 1054, 525, 540, 259, 266, 273, 280, 2583, 1302, 129, 132, 2835, 322, 705, 144, 3087, 1550, 3213, 260, 3339, 1674, 385, 392, 1539, 1798, 3717, 900, 3843, 1922, 3969, 128

Offset

1,2

Comments

By definition, sequence is injective (apart from possible 0's) and each a(n) is a multiple of n.

Links

Antti Karttunen, Table of n, a(n) for n = 1..4096

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) = n * A379228(n).

Prog

(PARI)
A048720(b, c) = fromdigits(Vec(Pol(binary(b))*Pol(binary(c)))%2, 2);
A065621(n) = bitxor(n-1, n+n-1);
memoA325567 = Map();
A325567(n) = if(1==n, 1, my(v); if(mapisdefined(memoA325567, n, &v), v, fordiv(n, d, if((d>1)&&A048720(A065621(n/d), d)==n, v = (n/d); break)); mapput(memoA325567, n, v); (v)));
A379126(n) = for(k=1, oo, if(A325567(k)==n, return(k)));

Crossrefs

Cf. A048720, A065621, A277320, A325567, A379128 (odd bisection), A379228 [= a(n)/n].

Cf. also A115872, A266195, A266351.

Sequence in context: A168175 A164382 A145521 * A230979 A145431 A196516

Adjacent sequences: A379123 A379124 A379125 * A379127 A379128 A379129

Keyword

nonn,new

Author

Antti Karttunen, Dec 21 2024

Status

approved