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

2, 3, 5, 7, 1, 11, 31, 71, 9, 23, 29, 313, 74, 14, 34, 75, 35, 96, 16, 77, 17, 37, 98, 38, 99, 710, 110, 310, 7109, 113, 12, 713, 1137, 13, 91, 4, 915, 115, 716, 316, 717, 317, 918, 119, 1193, 19, 719, 92, 112, 232, 27, 22, 923, 32, 39, 24, 125, 1257, 26

Offset: 1

Author

Yves Debeuret, Oct 10 2011

Keywords

• nonn
• base

Comments

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.

Examples

			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.
		

Links

• Paul Tek, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A032759, A228595.

Programs

Mathematica

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 *)

Python

from sympy import nextprime
from itertools import islice
def diggen():
    p = 2
    while True:
        yield from list(map(int, str(p)))
        p = nextprime(p)
def agen(): # generator of terms
    g = diggen()
    aset, nextd = set(), next(g)
    while True:
        an, nextd = nextd, next(g)
        while an in aset or nextd == 0:
            an, nextd = int(str(an) + str(nextd)), next(g)
        yield an
        aset.add(an)
print(list(islice(agen(), 80))) # Michael S. Branicky, Mar 31 2022