A320035 Indices (starting at 0) of integers in the increasing sequence S of nonnegative numbers that are representable in base 3/2 with digits {0, H=1/2, 1}.

0, 3, 11, 25, 46, 77, 117, 169, 232, 308, 401, 508, 631, 771, 929, 1108, 1308, 1527, 1767, 2029, 2315, 2626, 2961, 3325, 3719, 4138, 4585, 5057, 5561, 6094, 6658, 7251, 7880, 8543, 9245, 9982, 10760, 11572, 12419, 13305, 14226, 15181, 16177, 17209, 18285, 19404, 20560, 21760, 23007, 24297, 25637, 27027

Offset

1,2

Comments

Base 3/2 representations are considered with nonnegative exponents only (i.e. ending at the radix point).

Notice that this is not a positional number system as, for example, H0=3/4 < 1 (i.e., the lexicographical comparison of representations does not match the numerical comparison).

If we use base 3/2 with digits {0, 1, 2} instead (cf. A320272), this sequence correspond to the indices of even integers.

Links

Table of n, a(n) for n=1..52.

Formula

a(n) = number of positive numbers less than n that are representable in base 3/2 with digits {0, H=1/2, 1}. - Max Alekseyev, Oct 12 2018

a(n) = A320272(2*n-1).

Example

The sequence S starts with 0, H=1/2, H0=3/4, 1, H00=9/8, HH=5/4, 10=3/2, H0H=13/8, H000=27/16, ....
The indices of first two integers in S are a(1)=0 and a(2)=3.

Crossrefs

Bisection of A320272.

Sequence in context: A118436 A293413 A056106 * A147382 A212971 A258440

Adjacent sequences: A320032 A320033 A320034 * A320036 A320037 A320038

Keyword

base,nonn

Author

Tanya Khovanova and PRIMES STEP Junior group, Oct 03 2018

Extensions

Edited by Max Alekseyev, Oct 12 2018

Status

approved