cp's OEIS Frontend

A197124 Extract positive numbers from the infinite string of prime numbers 235711131719..., constructing the smallest numbers which have not appeared in an earlier extraction.

%I A197124 #24 Apr 01 2022 11:40:02
%S A197124 2,3,5,7,1,11,31,71,9,23,29,313,74,14,34,75,35,96,16,77,17,37,98,38,
%T A197124 99,710,110,310,7109,113,12,713,1137,13,91,4,915,115,716,316,717,317,
%U A197124 918,119,1193,19,719,92,112,232,27,22,923,32,39,24,125,1257,26
%N A197124 Extract positive numbers from the infinite string of prime numbers 235711131719..., constructing the smallest numbers which have not appeared in an earlier extraction.
%C A197124 The infinite stream of prime digits is basically chopped into slices such that each of the digits is used exactly once and the outcoming stream does not contain duplicates.
%H A197124 Paul Tek, <a href="/A197124/b197124.txt">Table of n, a(n) for n = 1..10000</a>
%e A197124 The initial digits 2, 3, 5, 7 and 1 are all extracted in the order of occurrence. The next 1 is rejected because it appeared earlier, and united with the (overall) third 1 to extract 11. The next 3 (from 13) appeared already earlier and is combined with the following 1 (from the 17) to created 31.
%t A197124 nn=100; digs = Flatten[Table[IntegerDigits[Prime[n]], {n, nn}]]; numList = {}; While[digs != {}, num = 0; While[num = num*10 + digs[[1]]; digs = Rest[digs]; newNum = ! MemberQ[numList, num]; (num == 0 || ! newNum) && digs != {}]; If[newNum, AppendTo[numList, num]]]; numList (* _T. D. Noe_, Oct 31 2011 *)
%o A197124 (Python)
%o A197124 from sympy import nextprime
%o A197124 from itertools import islice
%o A197124 def diggen():
%o A197124     p = 2
%o A197124     while True:
%o A197124         yield from list(map(int, str(p)))
%o A197124         p = nextprime(p)
%o A197124 def agen(): # generator of terms
%o A197124     g = diggen()
%o A197124     aset, nextd = set(), next(g)
%o A197124     while True:
%o A197124         an, nextd = nextd, next(g)
%o A197124         while an in aset or nextd == 0:
%o A197124             an, nextd = int(str(an) + str(nextd)), next(g)
%o A197124         yield an
%o A197124         aset.add(an)
%o A197124 print(list(islice(agen(), 80))) # _Michael S. Branicky_, Mar 31 2022
%Y A197124 Cf. A032759, A228595.
%K A197124 nonn,base
%O A197124 1,1
%A A197124 _Yves Debeuret_, Oct 10 2011