A367408 a(n) = n for n a power of 2; otherwise let 2^r be the greatest power of 2 which does not exceed n, then a(n) = the least novel m*a(k) where k = n - 2^r, and m is not a prior term.

1, 2, 3, 4, 5, 12, 18, 8, 6, 14, 21, 28, 35, 84, 126, 16, 7, 20, 27, 36, 45, 108, 162, 72, 54, 140, 189, 252, 315, 756, 1134, 32, 9, 22, 30, 40, 50, 120, 180, 80, 60, 154, 210, 280, 350, 840, 1260, 160, 70, 200, 270, 360, 450, 1080, 1620, 720, 540, 1400, 1890, 2520, 3150, 7560, 11340, 64, 10

Offset

1,2

Comments

Based on a recursion similar to that which produces the Doudna sequence, A005940, using the same definition of k, the "distance" from the greatest power of 2 less than n (compare with A365436).

Sequence is conjectured to be a permutation of the positive integers, A000027.

Links

Table of n, a(n) for n=1..65.

Formula

a(2^k) = 2^k for all k >= 0.

a(2^k + 1) = m, the least unused term up to a(2^k), where multiples (other than 1) of m have been used to generate terms between a(2^(k-1)) and a(2^k) except for those which have occurred earlier; see Example.

Example

a(3) = 3 since k = 1, a(1) = 1, and 3 is the smallest number which has not already occurred.
a(7) = 18, since k = 3, a(3) = 3, m = 6 is the least unused number and 18 has not already occurred.
For n = 18, k = 2, a(2) = 2, m = 9 is the least unused number, so we should expect a(18) = 2*9 = 18, but 18 has already occurred at a(7). Therefore we increment to m = 10, the next smallest unused number, and find a(18) = 20 (which has not occurred previously).

Prog

(PARI) lista(nn) = my(va=vector(nn)); for (n=1, nn, my(p=2^logint(n, 2)); if (p == n, va[n] = n, my(k=n-p, m=1); while (#select(x->(x==m), va) || #select(x->(x==m*va[k]), va), m++); va[n] = m*va[k]; ); ); va; \\ Michel Marcus, Dec 17 2023

Crossrefs

Cf. A005940, A053644, A365436.

Sequence in context: A093713 A057472 A333390 * A117577 A109849 A007662

Adjacent sequences: A367405 A367406 A367407 * A367409 A367410 A367411

Keyword

nonn

Author

David James Sycamore, Nov 17 2023

Status

approved