1,2

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.

David Applegate, Benoit Cloitre, Philippe DELEHAM 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.

David Applegate, Benoit Cloitre, Philippe DELEHAM and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers [pdf, ps].

a(n) = -n + Sum_{ k >= 1, k == n mod 2^k } 2^k. - N. J. A. Sloane (njas(AT)research.att.com) and David Applegate (david(AT)research.att.com), 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.

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;

Cf. A102370, A103530, A103581, A103582, A103583.

Sequence in context: A122264 A079824 A059329 this_sequence A007230 A059053 A032025

Adjacent sequences: A102368 A102369 A102370 this_sequence A102372 A102373 A102374

nonn

Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Feb 13 2005

More terms from Benoit Cloitre, Mar 20 2005

a(16) to a(22) from Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 21 2005

a(15) to a(29) from David Applegate (david(AT)research.att.com), Mar 22 2005