|
Search: id:A156695
|
|
|
| A156695 |
|
Odd numbers which are not of the form p + 2^a + 2^b, a, b > 0, p prime. |
|
+0
6
|
|
| 1, 3, 5, 6495105, 848629545, 1117175145, 2544265305, 3147056235, 3366991695, 3472109835, 3621922845, 3861518805, 4447794915, 4848148485, 5415281745, 5693877405, 6804302445, 7525056375, 7602256605, 9055691835, 9217432215
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
Crocker shows that this sequence is infinite.
All members above 5 found so far (up to 2.5 x 10^11) are divisible by 255 = 3 * 5 * 17, and many are divisible by 257. I conjecture that all members of this sequence greater than 5 are divisible by 255. This implies that all odd numbers (greater than 7) are the sum of a prime and at most three positive powers of two.
|
|
REFERENCES
|
Roger Crocker, "On the sum of a prime and of two powers of two", Pacific Journal of Mathematics 36:1 (1971), pp. 103-107.
Roger Crocker, Some counter-examples in the additive theory of numbers, Master's thesis (Ohio State University), 1962.
|
|
LINKS
|
Zhi-Wei Sun, Mixed Sums of Primes and Other Terms.
|
|
CROSSREFS
|
A118955
Sequence in context: A138154 A126334 A068635 this_sequence A154924 A071105 A104613
Adjacent sequences: A156692 A156693 A156694 this_sequence A156696 A156697 A156698
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Charles R Greathouse IV, Feb 13 2009
|
|
|
Search completed in 0.002 seconds
|
