cp's OEIS Frontend

A102371 Numbers missing from A102370.

%I A102371 #38 Mar 16 2021 16:37:29
%S A102371 1,2,7,12,29,62,123,248,505,1018,2047,4084,8181,16374,32755,65520,
%T A102371 131057,262130,524279,1048572,2097133,4194286,8388587,16777192,
%U A102371 33554409,67108842,134217711,268435428,536870885
%N A102371 Numbers missing from A102370.
%C A102371 Indices of negative numbers in A103122.
%C A102371 Write numbers in binary under each other; start at 2^k, read in upward direction with the first bit omitted and convert to decimal:
%C A102371 . . . . . . . . . . 0
%C A102371 . . . . . . . . . . 1
%C A102371 .. . . . . . . . . 10 < -- Starting here, the upward diagonal (first bit omitted) reads 1 -> 1
%C A102371 .. . . . . . . . . 11
%C A102371 . . . . . . . . . 100 < -- Starting here, the upward diagonal (first bit omitted) reads 10 -> 2
%C A102371 . . . . . . . . . 101
%C A102371 . . . . . . . . . 110
%C A102371 . . . . . . . . . 111
%C A102371 .. . . . . . . . 1000 < -- Starting here, the upward diagonal (first bit omitted) reads 111 -> 7
%C A102371 . . . . . . . . .1001
%C A102371 Thus a(n) = A102370(2^n - n) - 2^n.
%C A102371 Do we have a(n) = 2^n-1-A105033(n-1)? - _David A. Corneth_, May 07 2020
%H A102371 Reinhard Zumkeller, <a href="/A102371/b102371.txt">Table of n, a(n) for n = 1..1000</a>
%H A102371 David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers [<a href="http://neilsloane.com/doc/slopey.pdf">pdf</a>, <a href="http://neilsloane.com/doc/slopey.ps">ps</a>].
%H A102371 David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL8/Sloane/sloane300.html">Sloping binary numbers: a new sequence related to the binary numbers</a>, J. Integer Seq. 8 (2005), no. 3, Article 05.3.6, 15 pp.
%F A102371 a(n) = -n + Sum_{ k >= 1, k == n mod 2^k } 2^k. - _N. J. A. Sloane_ and _David Applegate_, Mar 22 2005. E.g. a(5) = -5 + 2^1 + 2^5 = 29.
%F A102371 a(2^k + k) -a(k) = 2^(2^k + k) - 2^k, with k>= 1.
%F A102371 a(1)=1, for n>1, a(n) = a(n-1) XOR (a(n-1) + n), where XOR is the bitwise exclusive-or operator. - _Alex Ratushnyak_, Apr 21 2012
%F A102371 a(n) = A105027(A000225(n)). - _Reinhard Zumkeller_, Jul 21 2012
%p A102371 A102371:= proc (n) local t1, l; t1 := -n; for l to n do if `mod`(n-l,2^l) = 0 then t1 := t1+2^l end if end do; t1 end proc;
%o A102371 (Python)
%o A102371 a=1
%o A102371 for n in range(2,66):
%o A102371     print(a, end=",")
%o A102371     a ^= a+n
%o A102371 # _Alex Ratushnyak_, Apr 21 2012
%o A102371 (Haskell)
%o A102371 a102371 n = a102371_list !! (n-1)
%o A102371 a102371_list = map (a105027 . toInteger) $ tail a000225_list
%o A102371 -- _Reinhard Zumkeller_, Jul 21 2012
%Y A102371 Cf. A102370, A103530, A103581, A103582, A103583, A105033.
%K A102371 nonn,base
%O A102371 1,2
%A A102371 _Philippe Deléham_, Feb 13 2005
%E A102371 More terms from _Benoit Cloitre_, Mar 20 2005
%E A102371 a(16)-a(22) from _Robert G. Wilson v_, Mar 21 2005
%E A102371 a(15)-a(29) from _David Applegate_, Mar 22 2005