cp's OEIS Frontend

A348710 In the binary expansion of n, decrease the length of each run of 1-bits by one.

%I A348710 #20 Mar 31 2024 19:04:26
%S A348710 0,0,0,1,0,0,2,3,0,0,0,1,4,2,6,7,0,0,0,1,0,0,2,3,8,4,4,5,12,6,14,15,0,
%T A348710 0,0,1,0,0,2,3,0,0,0,1,4,2,6,7,16,8,8,9,8,4,10,11,24,12,12,13,28,14,
%U A348710 30,31,0,0,0,1,0,0,2,3,0,0,0,1,4,2,6,7,0,0,0
%N A348710 In the binary expansion of n, decrease the length of each run of 1-bits by one.
%C A348710 Equivalently, change bits 01 -> 0, including a 0 reckoned above the most significant 1-bit of n so change there.
%C A348710 A single 1-bit run decreases to nothing.  The Fibbinary numbers (A003714) are those n with only single 1-bits so that a(n) = 0 iff n is in A003714.
%C A348710 a(n) = 1 iff n is in A213540 since those values end with bits 011 (which become 01) and otherwise have only single 1-bits, as do the Fibbinary numbers.
%C A348710 Decreasing each run is the inverse of the increase A175048 so that a(A175048(k)) = k.  This n = A175048(k) is the smallest n with a(n) = k and then other occurrences of k are by inserting single 1-bits into this n, including anywhere above the most significant bit.
%H A348710 Kevin Ryde, <a href="/A348710/b348710.txt">Table of n, a(n) for n = 0..10000</a>
%H A348710 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%e A348710 n    = 14551 = binary 111 000 11 0 1 0 111
%e A348710 a(n) =   787 = binary  11 000  1 0   0  11
%t A348710 Table[FromDigits[Flatten[Split@IntegerDigits[n,2]/. {1,a___}:>{a}],2],{n,0,82}] (* _Giorgos Kalogeropoulos_, Nov 01 2021 *)
%o A348710 (PARI) a(n) = my(v=binary(n),t=0); for(i=2,#v, if(v[i-1]||!v[i], v[t++]=v[i])); fromdigits(v[1..t],2);
%o A348710 (Python)
%o A348710 def a(n): return int(bin(n).replace("b", "").replace("01", "0"), 2)
%o A348710 print([a(n) for n in range(83)]) # _Michael S. Branicky_, Oct 31 2021
%Y A348710 Cf. A007088 (binary), A175048 (increase 1-bits), A090077 (decrease to single 1-bits).
%Y A348710 Cf. A003714 (indices of 0's), A213540 (indices of 1's).
%Y A348710 Cf. A106151 (decrease 0-bits), A318921 (decrease each run).
%K A348710 base,easy,nonn
%O A348710 0,7
%A A348710 _Kevin Ryde_, Oct 30 2021