Monday 14 August 2023

Biprimes and Permutations

I got to thinking today about biprimes, or semiprimes as they are also called, and how many have factors that are reversals of each other. Well, it doesn't take long to work that out using this code. Figure 1 shows the results up to one million (there are 18 numbers):


Figure 1

These numbers form part of OEIS A083815:


 A083815

Semiprimes whose prime factors are distinct and the reversal of one factor is equal to the other.


An extension of this idea to consider factors in which the digits of both factors are the same but permutations of each other. This would include all the numbers in OEIS A083815. Figure 2 shows the 79 numbers up to one million together with their factorisations (permalink):


Figure 2

Here are the numbers listed without the factorisation:

403, 1207, 2701, 7663, 14803, 23701, 26827, 34417, 35143, 35263, 40741, 43429, 54841, 62431, 70027, 73159, 75007, 89647, 99919, 101461, 102853, 103039, 103603, 117907, 125701, 127087, 128701, 130771, 140209, 141643, 146791, 150463, 153211, 173809, 174001, 182881, 191287, 197209, 201379, 205729, 212887, 230701, 232909, 246991, 247021, 249979, 257821, 273409, 280081, 293383, 295501, 297709, 302149, 326371, 342127, 355123, 367639, 371989, 374971, 382387, 386803, 394279, 427729, 428821, 436789, 453613, 462031, 469537, 503059, 565129, 589429, 643063, 690199, 692443, 698149, 743623, 778669, 824737, 910729

This sequence is not in the OEIS.

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