|
| |
|
|
A372588
|
|
Numbers k > 1 such that (greatest binary index of k) + (greatest prime index of k) is odd.
|
|
9
|
|
|
|
2, 6, 7, 8, 10, 11, 15, 18, 19, 21, 24, 26, 27, 28, 29, 32, 33, 34, 40, 41, 44, 45, 46, 47, 50, 51, 55, 59, 60, 62, 65, 70, 71, 72, 74, 76, 78, 79, 81, 84, 86, 87, 89, 91, 95, 96, 98, 101, 104, 105, 106, 107, 108, 111, 112, 113, 114, 116, 117, 122, 126, 128
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
A binary index of n is any position of a 1 in its reversed binary expansion. The binary indices of n are row n of A048793.
A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
|
|
|
LINKS
|
|
|
|
FORMULA
|
|
|
|
EXAMPLE
|
The terms (center), their binary indices (left), and their weakly decreasing prime indices (right) begin:
{2} 2 (1)
{2,3} 6 (2,1)
{1,2,3} 7 (4)
{4} 8 (1,1,1)
{2,4} 10 (3,1)
{1,2,4} 11 (5)
{1,2,3,4} 15 (3,2)
{2,5} 18 (2,2,1)
{1,2,5} 19 (8)
{1,3,5} 21 (4,2)
{4,5} 24 (2,1,1,1)
{2,4,5} 26 (6,1)
{1,2,4,5} 27 (2,2,2)
{3,4,5} 28 (4,1,1)
{1,3,4,5} 29 (10)
{6} 32 (1,1,1,1,1)
{1,6} 33 (5,2)
{2,6} 34 (7,1)
{4,6} 40 (3,1,1,1)
{1,4,6} 41 (13)
{3,4,6} 44 (5,1,1)
{1,3,4,6} 45 (3,2,2)
|
|
|
MATHEMATICA
|
Select[Range[2, 100], OddQ[IntegerLength[#, 2]+PrimePi[FactorInteger[#][[-1, 1]]]]&]
|
|
|
CROSSREFS
|
For just binary indices:
For just prime indices:
A070939 gives length of binary expansion.
Cf. A000720, A006141, A066208, A160786, A243055, A257991, A300272, A304818, A340604, A341446, A372429-A372433, A372438.
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
