A086697 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.

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

Offset: 1

Author

Shyam Sunder Gupta, Jul 28 2003

Keywords

• base
• nonn

Comments

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

Examples

			a(15)=146 is a term because 146, 46, 6 are all semiprimes.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)
• I. O. Angell and H. J. Godwin, On Truncatable Primes, Math. Comput. 31, 265-267, 1977.
• Index entries for sequences related to truncatable primes

Crossrefs

Cf. A001358 (semiprimes), A085733 (right-truncatable).

Programs

Mathematica

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 *)

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))
print(list(islice(agen(), 55))) # Michael S. Branicky, Aug 04 2022