OFFSET
1,2
COMMENTS
Indices of negative numbers in A103122.
Write numbers in binary under each other; start at 2^k, read in upward direction with the first bit omitted and convert to decimal:
. . . . . . . . . . 0
. . . . . . . . . . 1
.. . . . . . . . . 10 < -- Starting here, the upward diagonal (first bit omitted) reads 1 -> 1
.. . . . . . . . . 11
. . . . . . . . . 100 < -- Starting here, the upward diagonal (first bit omitted) reads 10 -> 2
. . . . . . . . . 101
. . . . . . . . . 110
. . . . . . . . . 111
.. . . . . . . . 1000 < -- Starting here, the upward diagonal (first bit omitted) reads 111 -> 7
. . . . . . . . .1001
Thus a(n) = A102370(2^n - n) - 2^n.
Do we have a(n) = 2^n-1-A105033(n-1)? - David A. Corneth, May 07 2020
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers [pdf, ps].
David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers, J. Integer Seq. 8 (2005), no. 3, Article 05.3.6, 15 pp.
FORMULA
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.
a(2^k + k) -a(k) = 2^(2^k + k) - 2^k, with k>= 1.
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
MAPLE
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;
PROG
(Python)
a=1
for n in range(2, 66):
print(a, end=", ")
a ^= a+n
# Alex Ratushnyak, Apr 21 2012
(Haskell)
a102371 n = a102371_list !! (n-1)
a102371_list = map (a105027 . toInteger) $ tail a000225_list
-- Reinhard Zumkeller, Jul 21 2012
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Philippe Deléham, Feb 13 2005
EXTENSIONS
More terms from Benoit Cloitre, Mar 20 2005
a(16)-a(22) from Robert G. Wilson v, Mar 21 2005
a(15)-a(29) from David Applegate, Mar 22 2005
STATUS
approved