OFFSET
1,3
COMMENTS
sum(k=1,n, a(k)*2^(k-1)) = 2^A089399(n)+1 for n>2, with a(1)=a(2)=1.
a(k) = 0 for k = 2, 10, 2058, 2058 + 2^2059, ..., that is, for k = A034797(n) - 1, n>=2. - Philippe Deléham, Nov 16 2007
FORMULA
EXAMPLE
Binary expansions of k*2^(k-1), with bits in ascending order by powers of 2, are:
1
001
0011
000001
0000101
00000011
000000111
00000000001
000000001001
0000000000101
00000000001101
000000000000011
0000000000001011
.................
Giving column sums:
10211132203222433...
MATHEMATICA
f[n_] := Block[{lg = Floor[Log[2, n]] + 1}, Sum[ Join[ Reverse[ IntegerDigits[n - i + 1, 2]], {0}][[i]], {i, lg}]]; Table[ f[n], {n, 105}] (* Robert G. Wilson v, Mar 26 2005 *)
PROG
(PARI) /* Prints initial 1000 terms: */
{A=vector(1000); for(n=1, #A, Bn=binary(n*2^(n-1)); for(k=1, min(#Bn, #A), A[k]=A[k]+Bn[#Bn-k+1]) ); print(A)}
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Paul D. Hanna, Oct 30 2003
STATUS
approved