A332815 a(n) = A108548(A005940(1+n)).

1, 2, 3, 4, 5, 6, 9, 8, 7, 10, 15, 12, 25, 18, 27, 16, 13, 14, 21, 20, 35, 30, 45, 24, 49, 50, 75, 36, 125, 54, 81, 32, 11, 26, 39, 28, 65, 42, 63, 40, 91, 70, 105, 60, 175, 90, 135, 48, 169, 98, 147, 100, 245, 150, 225, 72, 343, 250, 375, 108, 625, 162, 243, 64, 17, 22, 33, 52, 55, 78, 117, 56, 77, 130, 195, 84

Offset

0,2

Comments

This is variant of Doudna-sequence, A005940 and thus can be represented as a binary tree. Each child to the left is obtained by applying A332818 to the parent, and each child to the right is obtained by doubling the parent:

1

|

...................2...................

3 4

5......../ \........6 9......../ \........8

/ \ / \ / \ / \

/ \ / \ / \ / \

/ \ / \ / \ / \

7 10 15 12 25 18 27 16

13 14 21 20 35 30 45 24 49 50 75 36 125 54 81 32

etc.

Note the indexing: the sequence starts with a(0)=1, as is natural for sequences based on maps from base-2 expansion to prime factorization. This is

in contrast to A005940, which for historical reasons starts from offset 1.

For any n > 1, A332893(n) gives the value of the parent node. For any n >= 1, A332894(n) gives the distance to 1, and A332899(n) gives the number of odd numbers that occur (inclusively) on the path from 1 to n.

Links

Antti Karttunen, Table of n, a(n) for n = 0..8191

Antti Karttunen, Data supplement: n, a(n) computed for n = 0..65537

Index entries for sequences that are permutations of the natural numbers

Formula

a(n) = A108548(A005940(1+n)).

Prog

(PARI)
up_to = 26927;
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ From A005940
A108546list(up_to) = { my(v=vector(up_to), p, q); v[1] = 2; v[2] = 3; v[3] = 5; for(n=4, up_to, p = v[n-2]; q = nextprime(1+p); while(q%4 != p%4, q=nextprime(1+q)); v[n] = q); (v); };
v108546 = A108546list(up_to);
A108546(n) = v108546[n];
A108548(n) = { my(f=factor(n)); f[, 1] = apply(A108546, apply(primepi, f[, 1])); factorback(f); };
A332815(n) = A108548(A005940(1+n));

Crossrefs

Cf. A332816 (inverse permutation).

Cf. A005940, A108548, A332818, A332893, A332894, A332897, A332898, A332899.

Cf. A108546 (the left edge of the tree from 2 downward).

Sequence in context: A252753 A357268 A005940 * A355405 A372166 A005941

Adjacent sequences: A332812 A332813 A332814 * A332816 A332817 A332818

Keyword

nonn,tabf

Author

Antti Karttunen, Feb 28 2020

Status

approved