[seqfan] Re: Stacking binary blocks 100, 010, 001, 111

[mail at fumba.eu]

Zitat von "M. F. Hasler" <seqfan at hasler.fr>:

> Yes, that's obviously:
> Numbers having digits {1,2,4 or 7} in base 8.

Thank you- and you're right it should have been obvious :).

> So yes, it is a subsequence of numbers congruent to these modulo 8.
> To get the n-th term you can write n in base 4 and replace digits 0123 by
> 1247 and read the result in base 8
>
> In PARI/GP :
> is(n)=!#setminus(Set(digits(n,8)),[1,2,4,7])
> a(n,D=[1,2,4,7],b=8)=fromdigits(apply(d->D[d+1], digits(n,#D)),b)
>
> (This allows to produce the analog for any set of digits D and base b, by
> supplying either of these optional additional arguments.)
> --
> Maximilian
>
>
> On Mon, Feb 18, 2019, 06:55 Creigh wrote:
>
>> Dear Seqfans,
>>
>> While ordering a large matrix of "binary blocks" (see below, and
>> without going into technical details of why I was actually doing
>> that), it appeared I'd stumbled on the sequence A047541 (Numbers that
>> are congruent to {1, 2, 4, 7} mod 8) and I was happy to see the
>> explicit formula. However, these are not the same- the first deviation
>> appears on the 13th term. Any ideas for a formula? I assume proving
>> the sequence is a subset of A047541 is straightforward.
>>
>> Given the 4 binary blocks 100, 010, 001, 111 (or strings) and reading
>> backwards ignoring leading zeros, stack (concantenated with "_",
>> below) any number of these and order from least to greatest:
>>
>> 100 <-> 1
>> 010 <-> 2
>> 001 <-> 4
>> 111 <-> 7
>> 100_100 <-> 9
>> 010_100 <-> 10
>> 001_100 <-> 12
>> 111_100 <-> 15
>> 100_010 <-> 17
>> 010_010 <-> 18
>> 001_010 <-> 20
>> 111_010 <-> 23
>> 100_001 <-> 33
>> 010_001 <-> 34
>> 001_001 <-> 36
>> 111_001 <-> 39
>> 100_111 <-> 57
>> 010_111 <-> 58
>> 001_111 <-> 60
>> 111_111 <-> 63
>> 100_100_100 <-> 73
>> 010_100_100 <-> 74
>> 001_100_100 <-> 76
>> 111_100_100 <-> 79
>> 100_010_100 <-> 81
>> 010_010_100 <-> 82
>> 001_010_100 <-> 84
>> 111_010_100 <-> 87
>> 100_001_100 <-> 97
>> ...
>>
>> I'll wait for any replies and submit the sequence.
>>
>> Sincerely,
>> Creigh
>>
>>