Dubs theory problems

From the original thread:

- let к(n) be the number of bases in which n has dubs excluding base 1 and base n-1 as these are trivial, we shall call n a dubsless number if к(n)=0 and n>3

- the dubsless numbers up to 10000 are 5, 6, 29, 41, 61, 113, 317, 509, 569, 761, 797, 1213, 1229, 2617, 5297, 6221 and 8017. it turns out that all of these numbers except 6 are prime, and up to 10 million all except 6 are prime, we call these primes the ``dubsless primes'' a new kind of primes.

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This raised the following questions in the original thread:

- is 6 the only non prime dubsless number? SOLVED. ANSWER IS YES
- is the set of dubsless numbers/primes infinite? NOT SOLVED


I add one more open problem to the mysterious dubsless numbers:

- What is the sum of the inverses of all dubsless numbers (series 1/к(n))? If the set of dubsless number is infinite, does the series converge or diverge?

The sum of the first 10 million terms is about: 0.463697
The sum of the first 100 million terms is about: 0.463713

All dubs experts are asked to find a closed solution of the series if it converges.

- Also new ideas/open problems to the development of dubs theory are welcome. Dubs theory is currently stuck dealing only with dubsless numbers.

What are you babbling about? 1001 is the largest number.

>>2
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