A Special Class of Interprime

Sometimes mathematical properties can be represented effectively by means of visual aids. This can mean graphs of course but not exclusively. Take for example, OEIS A103741:

A103741

\(a(n)\) is a non-palindromic composite located between twin primes whose reverse, which is less than it, is also located between twin primes.

The number associated with my diurnal age today, 27240, is a member of this sequence because it is in between two adjacent primes, 27239 and 27241. When reversed to 4372, this reversal is also adjacent to two primes, namely 4371 and 4373. Visually this can be represented as shown in Figure 1 and it is quite effective. Notice how the reversal only works one way, from the larger number to the smaller and not vice versa, as shown by the directional arrows.

Figure 1

The initial members of this sequence are:

60, 240, 270, 600, 810, 822, 2130, 2340, 2802, 8010, 8220, 8430, 8838, 8862, 20550, 22740, 23202, 23370, 23910, 25410, 26880, 27240, 28410, 28572, 28662, 29022, 29760, 80472, 81702, 81930, 81972, 82140, 82530, 83220, 83340, 83640, 85620

What's interesting about this sequence is that there is a huge gap between 29760 and the next term 80472. This is more clearly seen in Figure 2 where the previous numbers have been plotted.

Figure 2

Figure 3 illustrates the number 80472 (not how the reversal here works both ways as shown by the directional arrows):

Figure 3

These types of interprimes thus fall into two categories: ones ending in 0 and ones ending in other digits. The former, like 27240, lead to interprimes that cannot then be reversed to return the original number. The latter, like 80472, lead to interprimes that can be reversed to return the original number.