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A137812 Left- or right-truncatable primes.

%I A137812 #53 Feb 16 2025 08:33:07
%S A137812 2,3,5,7,13,17,23,29,31,37,43,47,53,59,67,71,73,79,83,97,113,131,137,
%T A137812 139,167,173,179,197,223,229,233,239,271,283,293,311,313,317,331,337,
%U A137812 347,353,359,367,373,379,383,397,431,433,439,443,467,479,523,547,571
%N A137812 Left- or right-truncatable primes.
%C A137812 Repeatedly removing a digit from either the left or right produces only primes. There are 149677 terms in this sequence, ending with 8939662423123592347173339993799.
%C A137812 The number of n-digit terms is A298048(n). - _Jon E. Schoenfield_, Jan 28 2022
%H A137812 T. D. Noe, <a href="/A137812/b137812.txt">Table of n, a(n) for n = 1..10000</a>
%H A137812 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 A137812 T. D. Noe, <a href="/A137812/a137812.png">Plot of all terms</a>
%H A137812 Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_002.htm">Puzzle 2: Prime Strings</a>, The Prime Puzzles and Problems Connection.
%H A137812 Daniel Starodubtsev, <a href="/A137812/a137812_1.txt">Full sequence</a>
%H A137812 Eric Weisstein, <a href="https://mathworld.wolfram.com/TruncatablePrime.html">MathWorld: Truncatable Prime</a>
%H A137812 <a href="/index/Tri#tprime">Index entries for sequences related to truncatable primes</a>
%e A137812 139 is here because (removing 9 from the right) 13 is prime and (removing 1 from the left) 3 is prime.
%t A137812 Clear[s]; s[0]={2,3,5,7}; n=1; While[s[n]={}; Do[k=s[n-1][[i]]; Do[p=j*10^n+k; If[PrimeQ[p], AppendTo[s[n],p]], {j,9}]; Do[p=10*k+j; If[PrimeQ[p], AppendTo[s[n],p]], {j,9}], {i,Length[s[n-1]]}]; s[n]=Union[s[n]]; Length[s[n]]>0, n++ ];t=s[0]; Do[t=Join[t,s[i]], {i,n}]; t
%o A137812 (Python)
%o A137812 from sympy import isprime
%o A137812 def agen():
%o A137812     primes = [2, 3, 5, 7]
%o A137812     while len(primes) > 0:
%o A137812         yield from primes
%o A137812         cands = set(int(d+str(p)) for p in primes for d in "123456789")
%o A137812         cands |= set(int(str(p)+d) for p in primes for d in "1379")
%o A137812         primes = sorted(c for c in cands if isprime(c))
%o A137812 afull = [an for an in agen()]
%o A137812 print(afull[:60]) # _Michael S. Branicky_, Aug 04 2022
%Y A137812 Cf. A024770 (right-truncatable primes), A024785 (left-truncatable primes), A077390 (left-and-right truncatable primes), A080608.
%Y A137812 Cf. A298048 (number of n-digit terms).
%K A137812 base,fini,nonn
%O A137812 1,1
%A A137812 _T. D. Noe_, Feb 11 2008