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A085733 Right-truncatable semiprimes.

%I A085733 #43 Apr 03 2023 10:36:10
%S A085733 4,6,9,46,49,62,65,69,91,93,94,95,466,469,493,497,622,623,626,629,655,
%T A085733 694,695,697,698,699,913,914,917,933,934,939,943,949,951,955,958,959,
%U A085733 4661,4666,4667,4694,4699,4934,4939,4971,4979,6227,6233,6238
%N A085733 Right-truncatable semiprimes.
%C A085733 Semiprimes in which repeatedly deleting the rightmost digit gives a semiprime at every step until a single-digit semiprime remains.
%C A085733 The sequence is finite. According to Shyam Sunder Gupta the number 95861957783594714393831931415189937897 is the largest right-truncatable semiprime.
%C A085733 The total number of right-truncatable semiprimes including the single-digit semiprimes 4, 6 and 9 is 56076. - _Shyam Sunder Gupta_, Jan 13 2008
%C A085733 No term ends in (or contains) 0 else it would be divisible by 2, 5, and some other factor. - _Michael S. Branicky_, Aug 04 2022
%D A085733 Shyam Sunder Gupta, Truncatable semi-primes, Mathematical Spectrum 39:3 (2007), pp. 109-112.
%H A085733 Michael S. Branicky, <a href="/A085733/b085733.txt">Table of n, a(n) for n = 1..56076</a> (full sequence).
%H A085733 I. O. Angell and H. J. Godwin, <a href="https://doi.org/10.1090/S0025-5718-1977-0427213-2">On truncatable primes</a>, Math. Comput. 31:137, 265-267, 1977.
%H A085733 G. L. Honaker, Jr., <a href="https://t5k.org/curios/page.php?short=46613113151331733179">Prime Curios! 46613113151331733179</a>
%H A085733 Shyam Sunder Gupta, <a href="https://t5k.org/curios/page.php?curio_id=6861">The largest right-truncatable semiprime.</a> Prime Curios.
%H A085733 <a href="/index/Tri#tprime">Index entries for sequences related to truncatable primes</a>
%o A085733 (Python)
%o A085733 from sympy import factorint
%o A085733 from itertools import islice
%o A085733 def issemiprime(n): return sum(factorint(n).values()) == 2
%o A085733 def agen():
%o A085733     semis, digits = [4, 6, 9], "123456789" # can't end in 0
%o A085733     while len(semis) > 0:
%o A085733         yield from semis
%o A085733         cands = set(int(str(p)+d) for p in semis for d in digits)
%o A085733         semis = sorted(c for c in cands if issemiprime(c))
%o A085733 print(list(islice(agen(), 50))) # _Michael S. Branicky_, Aug 04 2022
%Y A085733 Cf. A001358, A213019, A086697.
%K A085733 nonn,base,fini,full
%O A085733 1,1
%A A085733 _G. L. Honaker, Jr._, Jul 20 2003
%E A085733 More terms from _Reinhard Zumkeller_, Jul 22 2003
%E A085733 More terms from _Hugo Pfoertner_, Jul 22 2003