A329873 a(n) is the number of distinct prime numbers whose binary digits appear in order but not necessarily as consecutive digits in the binary representation of n.
0, 0, 1, 1, 1, 3, 2, 2, 1, 3, 3, 5, 2, 5, 3, 2, 1, 4, 3, 6, 3, 6, 5, 6, 2, 5, 5, 6, 3, 6, 3, 3, 1, 4, 4, 7, 3, 9, 6, 7, 3, 8, 6, 9, 5, 8, 6, 8, 2, 6, 5, 7, 5, 8, 6, 8, 3, 6, 6, 9, 3, 8, 4, 3, 1, 4, 4, 8, 4, 9, 7, 9, 3, 11, 9, 11, 6, 11, 7, 10, 3, 8, 8, 12, 6
Offset: 0
Examples
The first terms, alongside the binary representations of n and of the corresponding prime numbers, are:
n a(n) bin(n) {bin(p)}
-- ---- ------ --------------------
0 0 0 {}
1 0 1 {}
2 1 10 {10}
3 1 11 {11}
4 1 100 {10}
5 3 101 {10, 11, 101}
6 2 110 {10, 11}
7 2 111 {11, 111}
8 1 1000 {10}
9 3 1001 {10, 11, 101}
10 3 1010 {10, 11, 101}
11 5 1011 {10, 11, 101, 111, 1011}
12 2 1100 {10, 11}
Links
- Rémy Sigrist, Table of n, a(n) for n = 0..16384
Programs
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Maple
b:= proc(n) option remember; `if`(n=0, {0}, map(x-> [x, 2*x+r][], b(iquo(n, 2, 'r')))) end: a:= n-> nops(select(isprime, b(n))): seq(a(n), n=0..84); # Alois P. Heinz, Jan 26 2022 -
PARI
a(n,base=2) = { my (b=digits(n,base), s=[0]); for (k=1, #b, s = setunion(s, apply(o -> base*o+b[k], s))); #select(isprime, s) }
Comments