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

1,1

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

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

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A226271 A137371 A179463 * A372533 A374739 A287568

Adjacent sequences: A086694 A086695 A086696 * A086698 A086699 A086700

Keyword

base,nonn

Author

Shyam Sunder Gupta, Jul 28 2003

Status

approved