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%I #15 Aug 02 2017 13:01:31
%S 2,3,13,23,31,41,43,241,421,431,1423,2143,2341,4231,5,53,251,521,523,
%T 541,1453,1523,1543,2153,2351,2531,2543,3251,3541,4153,4253,4513,4523,
%U 5231,5413,5431,61,163,263,461,463,563,613,631,641,643,653,3461,4261,4561,4621,4651,5261,5623,5641,6143,6421,6451
%N Ordered prime numbers as encountered from the building set of positive integers.
%C A permutation of the prime numbers.
%e The initial considered set is {1} which yields no primes. The next considered set is {1,2} which yields the prime 2. The next evaluation from {1,2,3} yields 3,13,23,31. Note that no considered integer is used more than once, so 11 is not added from {1,2,3}. Primes are ordered within each considered set. Thus we know the next sequence member after considering {1,2,3,4,5,6} will be 7. Note also that digits are not pulled from any subset element. Treating {1,2,...10} the 10 is not parsed or broken up, just considered in its entirety.
%t a = {}; Do[s = Select[ FromDigits /@ Flatten[ Permutations /@ Subsets[ Flatten[ IntegerDigits /@ Range[n]]], 1], PrimeQ]; a = Join[a, Union@ Complement[s, a]], {n, 6}]; a (* _Giovanni Resta_, Jun 05 2017 *)
%o (Ruby)
%o require 'prime'
%o maxx=6
%o j5=1
%o myList=Array.new()
%o interm=Array.new()
%o final=Array.new()
%o myList[j5-1]=j5
%o while j5<maxx do
%o ...j5+=1
%o ...myList[j5-1]=j5
%o ...if Prime.prime?(j5)==true
%o ......ptr=final.length
%o ......final[ptr]=j5
%o ...end
%o ...for i5 in 2..myList.length
%o ......interm=myList.repeated_permutation(i5).to_a
%o ......for k5 in 0..interm.length-1
%o .........temp=''
%o .........for m5 in 0..i5-1
%o ............temp= [temp,interm[k5][m5].to_s].join
%o .........end
%o .........substr=j5.to_s
%o .........aok=1
%o .........for z in 0..temp.length-1
%o ............for w in 0..temp.length-1
%o ...............if z==w
%o ..................next
%o ...............elsif temp[z]==temp[w]
%o ..................aok=0
%o ..................break
%o ...............end
%o ............end
%o .........end
%o .........if aok>0 && Prime.prime?(temp.to_i)== true && temp.include?(substr)
%o ............ptr=final.length
%o ............final[ptr]=temp.to_i
%o .........end
%o ......end
%o ...end
%o end
%o p final
%Y Cf. A000040.
%K base,easy,nonn
%O 1,1
%A _Bill McEachen_, Jun 04 2017
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