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A197124
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Extract positive numbers from the infinite string of prime numbers 235711131719..., constructing the smallest numbers which have not appeared in an earlier extraction.
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3
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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
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graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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 *)
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PROG
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(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)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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