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%I #25 Aug 05 2022 07:46:12
%S 4,6,9,14,26,34,39,46,49,69,74,86,94,134,146,169,194,214,226,249,274,
%T 314,326,334,339,346,386,394,446,469,514,526,586,614,626,634,649,669,
%U 674,694,734,746,749,794,849,869,886,914,926,934,939,949,974,1169,1214
%N 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.
%C 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
%H Michael S. Branicky, <a href="/A086697/b086697.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harvey P. Dale)
%H I. O. Angell and H. J. Godwin, <a href="http://dx.doi.org/10.1090/S0025-5718-1977-0427213-2">On Truncatable Primes</a>, Math. Comput. 31, 265-267, 1977.
%H <a href="/index/Tri#tprime">Index entries for sequences related to truncatable primes</a>
%e a(15)=146 is a term because 146, 46, 6 are all semiprimes.
%t 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 *)
%t 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 *)
%o (Python)
%o from sympy import factorint
%o from itertools import islice
%o def issemiprime(n): return sum(factorint(n).values()) == 2
%o def agen():
%o semis, digits = [4, 6, 9], "123456789" # can't have 0
%o while len(semis) > 0:
%o yield from semis
%o cands = set(int(d+str(p)) for p in semis for d in digits)
%o semis = sorted(c for c in cands if issemiprime(c))
%o print(list(islice(agen(), 55))) # _Michael S. Branicky_, Aug 04 2022
%Y Cf. A001358 (semiprimes), A085733 (right-truncatable).
%K base,nonn
%O 1,1
%A _Shyam Sunder Gupta_, Jul 28 2003
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