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Template:Sequence of the Day for November 18
From OeisWiki
Intended for: November 18, 2013
Timetable
- First draft entered by Alonso del Arte on October 17, 2012 ✓
- Draft to be reviewed by September 18, 2013
- Draft to be approved by October 18, 2013
Yesterday's SOTD * Tomorrow's SOTD |
The line below marks the end of the <noinclude> ... </noinclude> section.
p + 2 b 2 |
p |
b > 0 |
- { 1, 3, 17, 137, 227, 977, 1187, 1493, 5777, 5993, ¿...? }
On November 18, 1752, Christian Goldbach wrote a letter to Leonhard Euler in which he conjectured that every odd integer can be expressed as the sum of a prime and twice a square. Euler verified this lesser known conjecture of Goldbach’s up to 2500 and found no counterexamples. Goldbach did allow the square to be zero and considered 1 a prime number, and thus 3, 5, 7 are taken care of with 0 2, 9 = 1 + 2 × 2 2 or 7 + 2 × 1 2, etc.
When Moritz Stern read the Goldbach–Euler correspondence, he became interested in this problem and checked up to 9000, finding the composite numbers 5777 and 5993. With 5777, we can now quickly verify that not only is each5777 − 2 b 2 |
b > 0 |
p + 2 b 2 |
With modern computers, M. F. Hasler and Benjamin Chaffin have verified there are no more terms up to 2 × 10 13.