Problems & Puzzles: Puzzles

 Puzzle 825. Primes type Liouville For sure you already know the Liouville's constant. L=Σ10^(-n!), for n=1 to ∞ = 0.110001000000000000000001... " Liouville's constant is a decimal fraction with a 1 in each decimal place corresponding to a factorial , and zeros everywhere else. " [see 1], where n!=1,2,6,24,120,720... Based in this definition, I produce the following new definition producing a sequence of integers: NL(n)= Σ10^(i!-1), for i=1 to n; for n=1 to ∞. NL(1)=1 NL(2)=11 NL(3)=100011 NL(4)=100000000000000000100011 ... Q1. Find the first three prime NL numbers Q2. Redo Q1 for R(NL). R(NL) means "the reverse of NL".

Contribution came from T. D. Noe

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Tony wrote:

Q1. The only known prime in the NL sequence is 11.
In http://www.integersequences.org/s000860.html I list the smallest factor
in the first 33 terms of the NL sequence.

Q2. The only known prime in the RNL sequence is 11.
In http://www.integersequences.org/s000861.html I list the smallest factor
in the first 24 terms of the RNL sequence.

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