OFFSET
1,2
COMMENTS
This sequence has similarities with A175428: here a(n) XOR a(n+1) is a cube, there a(n) + a(n+1) is a cube.
This sequence is conjectured to the a permutation of the natural numbers.
The first fixed points are: 1, 5676, 5677, 5698, 11677, 13226, 26943, 26946, 27575, 28039, 28569, 28625, 30127, 30162, 37660, 37661, 44672, 44673, 45934.
The scatterplot of the first terms of the sequence shows hatches (see Links section).
LINKS
Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, Scatterplot of the first 50000 terms
EXAMPLE
The first terms, alongside a(n) XOR a(n+1), are:
n a(n) a(n) XOR a(n+1)
-- ---- ---------------
1 1 2^3
2 9 1^3
3 8 3^3
4 19 1^3
5 18 2^3
6 26 1^3
7 27 4^3
8 91 5^3
9 38 1^3
10 39 2^3
11 47 1^3
12 46 3^3
13 53 1^3
14 52 2^3
15 60 1^3
16 61 5^3
17 64 1^3
18 65 2^3
19 73 1^3
20 72 3^3
PROG
(PARI) seen = 0; unseen = 1
other(p) = seen += 2^p; while (bittest(seen, unseen), unseen++); \
for (v=unseen, oo, if (!bittest(seen, v) && ispower(bitxor(p, v), 3), return (v)))
for (n=1, 57, v=if (n==1, 1, other(v)); print1 (v ", "))
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Dec 17 2017
STATUS
approved