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%I #11 Sep 08 2013 19:54:50
%S 6,13,12,11,10,25,24,31,30,21,20,19,18,17,16,23,22,29,28,59,58,41,40,
%T 47,46,37,36,35,34,33,32,39,38,45,44,43,42,57,56,63,62,53,52,51,50,49,
%U 48,119,118,125,124,91,90,73,72,79,78,69,68,67,66,65,64,71,70,77,76,75,74
%N Write numbers 0, 1, 2, ... in binary under each other, right-adjusted; shift the 2^k's column upwards by prime(k+1) places (for k >= 0); read the resulting array across rows starting at the (old) zero row; convert to decimal.
%H 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>].
%F a(n) = Sum_{k >= 0} 2^k*(1-(-1)^floor((n+prime(k+1))/2^k))/2.
%e The array before the columns are shifted upwards:
%e --------- <- the "zero" line
%e ....00000
%e ....00001
%e ....00010
%e ....00011
%e ....00100
%e ....00101
%e ....00110
%e ....00111
%e ....01000
%e .........
%e After the upwards shifts:
%e ....0
%e ....0
%e ....0
%e ....0
%e ....00
%e ....00
%e ....000
%e ....000
%e ....0000
%e ....00000
%e ....00111
%e --------- <- the "zero" line
%e ....00110 = 6
%e ....01101 = 13
%e ....01100 = 12
%e ....01011 = 11
%e ....01010 = 10
%e ....11001 = 25
%e ....11000 = 24
%e ....11111 = 31
%e ....11110 = 30
%e .........
%o (PARI) {a(n) = local(s, m, k); s=0;k=0;while(1,m=floor((n+prime(k+1))/2^k);if(m==0,return(s));if(m%2,s+=2^k);k++)} (Alekseyev)
%Y Cf. A102370.
%K nonn,easy,base
%O 0,1
%A _N. J. A. Sloane_ and _Philippe Deléham_, Feb 13 2005
%E More terms from _Max Alekseyev_, May 17 2005