A305410 a(1) = 1, and for any n > 0, a(2*n) = a(n) + k(n) and a(2*n+1) = a(n) + 2 * k(n) where k(n) is the least positive integer not leading to a duplicate term.
1, 2, 3, 4, 6, 5, 7, 8, 12, 10, 14, 9, 13, 11, 15, 16, 24, 17, 22, 18, 26, 21, 28, 19, 29, 20, 27, 23, 35, 30, 45, 25, 34, 31, 38, 32, 47, 33, 44, 36, 54, 37, 48, 39, 57, 40, 52, 41, 63, 42, 55, 43, 66, 46, 65, 49, 75, 51, 67, 50, 70, 53, 61, 56, 87, 58, 82
Offset: 1
Keywords
Examples
The first terms, alongside k(n) and associate children, are: n a(n) k(n) a(2*n) a(2*n+1) -- ---- ---- ------ -------- 1 1 1 2 3 2 2 2 4 6 3 3 2 5 7 4 4 4 8 12 5 6 4 10 14 6 5 4 9 13 7 7 4 11 15 8 8 8 16 24 9 12 5 17 22 10 10 8 18 26
Links
- Rémy Sigrist, Table of n, a(n) for n = 1..10000
- Rémy Sigrist, Scatterplot of (n, a(n)) for n = 1..10000000
Crossrefs
This sequence is a variant of A322510.
Programs
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PARI
lista(nn) = my (a=[1], s=2^a[1]); for (n=1, ceil(nn/2), for (k=1, oo, if (!bittest(s, a[n]+k) && !bittest(s, a[n]+2*k), a=concat(a, [a[n]+k, a[n]+2*k]); s+=2^(a[n]+k) + 2^(a[n]+2*k); break))); a[1..nn]
Formula
a(n) = 2*a(2*n) - a(2*n + 1).
Extensions
Name corrected by Rémy Sigrist, Apr 26 2020
Comments