A391729 a(n) = Sum_{k=1..A003817(n)} [A048720(A065621(n),k) == n*k], where [ ] is the Iverson bracket.

1, 3, 1, 7, 1, 3, 1, 15, 1, 3, 4, 6, 3, 3, 1, 31, 1, 3, 4, 6, 1, 8, 4, 10, 1, 7, 1, 6, 1, 3, 1, 63, 1, 3, 4, 6, 5, 7, 8, 10, 1, 3, 12, 14, 1, 7, 4, 16, 3, 3, 1, 15, 1, 3, 5, 10, 7, 3, 1, 6, 3, 3, 1, 127, 1, 3, 4, 6, 5, 7, 8, 10, 1, 9, 4, 12, 5, 12, 8, 15, 3, 3, 6, 6, 1, 21, 4, 21, 1, 3, 6, 12, 1, 7, 4, 26, 1, 7, 1

Offset

1,2

Comments

a(n) gives the index (column number) of A003817(n) on the row n of array A115872.

Links

Antti Karttunen, Table of n, a(n) for n = 1..16383

Index entries for sequences defined by congruent products between domains N and GF(2)[X]

Index entries for sequences related to binary expansion of n.

Index entries for sequences related to carryless arithmetic.

Formula

For all n >= 1, A115872(n, a(n)) = A003817(n).

Prog

(PARI)
A003817(n) = (1<<(log(2*n+1)\log(2)))-1;
A006068(n) = { my(s=1, ns); while(1, ns = n >> s; if(0==ns, return(n)); n = bitxor(n, ns); s <<= 1); };
A048720(b, c) = fromdigits(Vec(Pol(binary(b))*Pol(binary(c)))%2, 2);
A391729(n) = sum(k=1, A003817(n), my(t=bitxor(k, k*n)); (!(hammingweight(t)%2) && A006068(t) == 2*A048720(k, n-1))); \\ Why this works? See comments in A115873.

Crossrefs

Cf. A003817, A048720, A065621, A115873, A391590 (positions of 1's).

Cf. array A115872.

Sequence in context: A053381 A038712 A354587 * A065745 A361438 A268670

Adjacent sequences: A391726 A391727 A391728 * A391730 A391731 A391732

Keyword

nonn,base

Author

Antti Karttunen, Dec 20 2025

Status

approved