# [seqfan] New sequence and a 3D graph

John W. Nicholson reddwarf2956 at yahoo.com
Mon Feb 20 02:19:41 CET 2012

```I hope I can get some help doing the following because I am poor at writing programs in more than one way. One I don't have the money, and two I don't have the experience.  What I do is import a sequence into Open Office spreadsheet and compare/calulate values. This is very limited in data and speed, but allow me to see things overlooked by others. I also do have pari/GP and can run scripts. However, I have not come up with a script to do the following:

1.
I would like to see a 3D graph of  x = A182873, y = A190874, and z = the number of times an intersection of (x,y) is used. Color can also be used to show where the last z-number occurred. For example, the value at (4,9) would have the color of first and last least use because there is only one *odd gap* between two Ramanujan primes; namely the one between 2 and 11. While (1,2) {Twins Ramanujan primes} would have a color of currently used because there are a lot of twin Ramanujan primes. (It would be really cool if a special color is used for when a maximal prime gap, A002386 and 2*A002386, occurs.)

A plot2 graph using n<= 10000 showing the 2D,  x = A182873, y = A190874, of this graph:

The file with the 3D graph should be able to be added list of links within the sequences A182873 and A190874.

2.
I realize that A165959 is the smallest values of an inequality (see http://en.wikipedia.org/wiki/Ramanujan_prime#Ramanujan_prime_corollary, A168421 and A168425) linked from each Ramanujan prime, A104272, to the next. I know that some Ramanujan primes are twin Ramanujan primes, so there is only one term between (R_n,R_(n+1)] and it is R_(n+1). For others, I know that there are multiple terms term between (R_n,R_(n+1)] . A new sequence is needed for these terms using A165959 as the first column. In effect, this new sequence proves a sharp upper bounds to all of the term values of A000040, prime numbers, but in a tabf table of increasing values depending on the values of  A168421, A104272, A182873 and A190874.

John W. Nicholson

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