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A055521 Restricted left truncatable (Henry VIII) primes.

%I A055521 #28 Feb 16 2025 08:32:42
%S A055521 773,3373,3947,4643,5113,6397,6967,7937,15647,16823,24373,33547,34337,
%T A055521 37643,56983,57853,59743,62383,63347,63617,69337,72467,72617,75653,
%U A055521 76367,87643,92683,97883,98317,121997,124337,163853,213613,236653
%N A055521 Restricted left truncatable (Henry VIII) primes.
%C A055521 There are 1440 such primes, the largest being 357686312646216567629137.
%C A055521 Left-truncatable primes (A024785) which have at least two digits and are not the end of a larger left-truncatable prime. - _Jens Kruse Andersen_, Jul 29 2014
%D A055521 Kahan, S. and Weintraub, S. "Left Truncatable Primes." J. Recr. Math. 29, 254-264, 1998.
%H A055521 Jens Kruse Andersen, <a href="/A055521/b055521.txt">Table of n, a(n) for n = 1..1440</a> (complete sequence)
%H A055521 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 A055521 James Grime and Brady Haran, <a href="https://www.youtube.com/watch?v=azL5ehbw_24">357686312646216567629137</a>, Numberphile video (2018)
%H A055521 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TruncatablePrime.html">Truncatable Prime</a>
%H A055521 <a href="/index/Tri#tprime">Index entries for sequences related to truncatable primes</a>
%e A055521 773 is in the sequence since 773, 73, 3 are primes, while no digit 1..9 gives a prime if placed before 773. 13 is not in the sequence since for example 113 is prime. 2 and 5 are disqualified for only having one digit. - _Jens Kruse Andersen_, Jul 29 2014
%o A055521 (Python)
%o A055521 from sympy import isprime, primerange
%o A055521 def afull():
%o A055521     alst, prime_strs, an, digits = [], ["2", "3", "5", "7"], 0, 1
%o A055521     while len(prime_strs) > 0:
%o A055521         new_prime_strs = set()
%o A055521         for p in prime_strs:
%o A055521             can_extend = False
%o A055521             for d in "123456789":
%o A055521                 c = d + p
%o A055521                 if isprime(int(c)):
%o A055521                     can_extend = True
%o A055521                     new_prime_strs.add(c)
%o A055521             if digits > 1 and not can_extend:
%o A055521                 alst.append(int(p))
%o A055521         prime_strs = new_prime_strs
%o A055521         digits += 1
%o A055521     return sorted(alst)
%o A055521 print(afull()) # _Michael S. Branicky_, Dec 11 2022
%Y A055521 Cf. A024785.
%K A055521 nonn,base,fini,full
%O A055521 1,1
%A A055521 _Eric W. Weisstein_