[seqfan] Two consecutive integers sum to a prime

[franktaw at netscape.net]

Here's (to me) a more interesting question relating to A055265: which 
primes are not represented as the sum of consecutive terms?  This 
starts:

2, 197, 199, 317, 467, 563, 599, 653, 811, 829, 863, 977, 1019, 1039, 
1093, 1097, 1103, 1327, 1373, 1429, 1433, 1607, 1609, 1613, 1669, 1877, 
1879

This is based on looking at the first 1000 terms of A055265; to that 
point, the largest missing integer was 992, so no prime less than 1984 
could still occur.  1993 and 1999 had not yet occurred, but might yet.

I find it intriguing how many of the early primes occur.  I was about 
ready to conjecture that every odd prime occurs (looking at the first 
100 terms of A055265), but decided to look a bit further.

Also note the twin prime occurrences: 197 & 199, 1607 & 1609, 1877 & 
1879.  That's a lot for so few primes of this size.  There does seem to 
be some clustering effect: you get a lot of pairs summing to a small 
cluster of primes, and then the integers in that range are exhausted 
and you get a jump to a higher level.

Franklin T. Adams-Watters

-----Original Message-----
From: Eric Angelini <Eric.Angelini at kntv.be>

...

Based on:
http://www2.research.att.com/~njas/sequences/A055265