A391588 a(n) = A003817(n) XOR (A003817(n)*n).

0, 5, 10, 27, 36, 45, 54, 119, 136, 153, 170, 187, 204, 221, 238, 495, 528, 561, 594, 627, 660, 693, 726, 759, 792, 825, 858, 891, 924, 957, 990, 2015, 2080, 2145, 2210, 2275, 2340, 2405, 2470, 2535, 2600, 2665, 2730, 2795, 2860, 2925, 2990, 3055, 3120, 3185, 3250, 3315, 3380, 3445, 3510, 3575, 3640, 3705, 3770

Offset

1,2

Comments

From the equivalences of the formulas a(n) = A003817(n) XOR (A003817(n)*n) and a(n) = A048724(A048720(n-1, A003817(n))) [the latter can be rewritten as A048720(n-1,A048724(A003817(n))), which is easily seen to be equivalent with the other given formulas for this sequence] follows that A003817(n) gives a guaranteed upper bound for A115873(n). See comments in the latter sequence.

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

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

a(n) = ((n-1) * 2^A070939(n)) + n-1 = A087737(n-1)-1.

If n is not in A000079, then a(n) = A020330(n-1).

a(n) = A048724(A048720(n-1, A003817(n))) = A048720(n-1, A048724(A003817(n))).

Prog

(PARI)
A003817(n) = (1<<(log(2*n+1)\log(2)))-1;
A391588(n) = bitxor(A003817(n), A003817(n)*n);
(PARI)
A070939(n) = if(!n, 1, #binary(n));
A391588(n) = ((2^A070939(n)*(n-1))+n-1);
(PARI)
A003817(n) = (1<<(log(2*n+1)\log(2)))-1;
A048720(b, c) = fromdigits(Vec(Pol(binary(b))*Pol(binary(c)))%2, 2);
A048724(n) = bitxor(n, 2*n);
A391588(n) = A048724(A048720(n-1, A003817(n)));
A391588(n) = A048720(n-1, A048724(A003817(n))); \\ Alternatively

Crossrefs

Cf. A003817, A003987, A048720, A048724, A115873, A391589.

Cf. A000079, A020330, A087737.

Sequence in context: A277825 A390554 A054298 * A022094 A134129 A240515

Adjacent sequences: A391585 A391586 A391587 * A391589 A391590 A391591

Keyword

nonn,base

Author

Antti Karttunen, Dec 20 2025

Status

approved