A379128 -id:A379128 - cp's OEIS frontend

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

Antti Karttunen, Dec 21 2024

nonn

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

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

Cf. also A115872, A266195, A266351.

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)));

a(n) = n * A379228(n).

A379127 a(1) = 1; for n > 1, a(n) is the largest proper divisor d of 2n-1 such that A048720(A065621(d),(2n-1)/d) is equal to 2n-1.

Original entry on oeis.org

1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 11, 5, 1, 1, 1, 1, 3, 1, 7, 1, 1, 1, 1, 1, 1, 1, 13, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 43, 1, 19, 9, 1, 1, 1, 1, 1, 1, 1, 1, 3, 5, 1, 1, 23, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 13, 1, 1, 1, 1, 1, 1, 1

Offset: 1

Antti Karttunen, Dec 21 2024

nonn

The position of the first occurrence of odd numbers k = 1, 3, 5, 7, 9, ... in this sequence is given by (1/2) * (A379128(2*k-1)+1).

Odd bisection of A325567.

Cf. A048720, A065621, A277320, A379128.

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))));
A379127(n) = A325567(2*n-1);

a(n) = A325567(2*n-1).

cp's OEIS Frontend

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.

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