Intended for: February 5, 2013
Timetable
- First draft entered by Alonso del Arte on November 3, 2011 based on remarks from Zhi Wei-Sun ✓
- Draft reviewed by Alonso del Arte on December 1, 2012 ✓
- Draft to be approved by January 5, 2012
Yesterday's SOTD * Tomorrow's SOTD
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A157218: Number of ways to write the
-th positive odd integer in the form
with
a prime congruent to
1 mod 6 and
,
positive integers.
-
{ ... 0, 1, 1, 0, 2, 1, 0, 2, 3, 1, ... }
In 2009, Zhi-Wei Sun conjectured that
for all
; in other words, any odd integer greater than
34 can be written as the sum of a prime congruent to
1 mod 6, a positive power of
2 and seven times a positive power of
2. Sun verified the conjecture for odd integers below
5 × 10 7, and Qing-Hu Hou continued the verification for odd integers below
1.5 × 10 8 (on Sun’s request). Compare the conjecture with R. Crocker’s result that there are infinitely many positive odd integers not of the form
with
an odd prime and
,
positive integers.