[seqfan] Re: More stupid thingies with commas, sums & primes

[Christopher Hunt gribble]

My C++ program halts with a stack overflow exception for n = 100000.
However, for n = 10000 and 20000 the prime sum frequencies are:


  2      773    2762
  3      483    1315
  5    1219    3051
  7    1835    3835
11    3720    6732
13    1197    1362
17      772      942

The frequencies with which the partitions of the prime sums into the least
significant digit (LSD) of a(n-1) and the most significant digit (MSD) of
a(n) are for n = 10000:

       MSD     0       1      2       3       4      5       6       7
8       9
LSD
 0                  0       0  273  219       0  225       0  284       0
0
 1                  0  500       1       0  198       0  303       0       0
0
 2                  0  263       0  209       0  227       0       0       0
302
 3                  0       0  323       0  207       0       0       0  471
0
 4                  0  264       0  209       0       0       0  511       0
17
 5                  0       0  325       0       0       0  507       0  168
0
 6                  0  280       0       0       0  436       0  284       0
0
 7                  0       0       0       0  698       0  301       0
0       0
 8                  0       0       0  474       0  223       0       0
0  300
 9                  0       0  321       0  204       0       0       0  472
0

and for n = 20000:

       MSD     0       1      2       3       4      5       6       7
8       9
LSD
 0                  0       0 1262  219     0   225      0   295       0
0
 1                  0 1500      1      0  198       0  303       0        0
0
 2                  0 1095      0  209      0  227       0       0        0
469
 3                  0       0 1322     0  207       0       0       0   471
0
 4                  0 1097      0  209      0       0       0  522        0
172
 5                  0       0 1325     0       0       0  507       0   168
0
 6                  0 1269      0      0       0  436       0  294        0
0
 7                  0       0       0       0 1698     0  301       0
0       0
 8                  0       0       0 1306     0   223     0        0
0  470
 9                  0       0 1323      0  204      0      0        0  472
0

It is interesting to note that some frequencies have not changed.

For n = 10000:
The smallest integer not present in the first 10000 terms = 7968
The largest integer present in the first 10000 terms            = 40195

For n = 20000:
The smallest integer not present in the first 20000 terms = 13851
The largest integer present in the first 20000 terms            = 41195

Chris

-----Original Message-----
From: seqfan-bounces at list.seqfan.eu [mailto:seqfan-bounces at list.seqfan.eu]
On Behalf Of Ed Jeffery
Sent: 19 October 2011 4:46 PM
To: seqfan at list.seqfan.eu
Subject: [seqfan] Re: More stupid thingies with commas, sums & primes

Then what about the graph of Chris' results for the distribution as n
becomes large: does it increase and peak at the prime 7 (the midpoint
between the primes 2 and 17) and is it symmetrical about the prime 7? -- Ed
Jeffery

>The frequencies of occurrence of the 7 prime sums over the first 10000
terms
>are:
>2    1788448
>3    2318299
>5    3624036
>7    4340644
>11    4100476
>13    2246844
>17     503513
>suggesting non-uniformity of distribution.

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