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A086697
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Left-truncatable semiprimes, i.e., semiprimes in which repeatedly deleting the leftmost digit gives a semiprime at every step until a single-digit semiprime remains.
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2
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4, 6, 9, 14, 26, 34, 39, 46, 49, 69, 74, 86, 94, 134, 146, 169, 194, 214, 226, 249, 274, 314, 326, 334, 339, 346, 386, 394, 446, 469, 514, 526, 586, 614, 626, 634, 649, 669, 674, 694, 734, 746, 749, 794, 849, 869, 886, 914, 926, 934, 939, 949, 974, 1169, 1214
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OFFSET
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1,1
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COMMENTS
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Zero digits are not permitted, so 106 is not a member even though 106 and 6 are both semiprimes. - Harvey P. Dale, Jun 28 2017
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LINKS
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EXAMPLE
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a(15)=146 is a term because 146, 46, 6 are all semiprimes.
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MATHEMATICA
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ltsQ[n_]:=DigitCount[n, 10, 0]==0&&AllTrue[FromDigits/@NestList[Rest[ #]&, IntegerDigits[n], IntegerLength[n]-1], PrimeOmega[#]==2&]; Select[ Range[ 1500], ltsQ] (* Harvey P. Dale, Jun 28 2017 *)
lt3pQ[n_]:=Module[{idn=IntegerDigits[n]}, FreeQ[idn, 0]&&Union[PrimeOmega/@(FromDigits/@Table[Take[idn, -i], {i, Length[idn]}])]=={2}]; Select[Range[8000], lt3pQ] (* Vincenzo Librandi, Apr 22 2018 *)
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PROG
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(Python)
from sympy import factorint
from itertools import islice
def issemiprime(n): return sum(factorint(n).values()) == 2
def agen():
semis, digits = [4, 6, 9], "123456789" # can't have 0
while len(semis) > 0:
yield from semis
cands = set(int(d+str(p)) for p in semis for d in digits)
semis = sorted(c for c in cands if issemiprime(c))
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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STATUS
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approved
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