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 A137812 Left- or right-truncatable primes. 11
 2, 3, 5, 7, 13, 17, 23, 29, 31, 37, 43, 47, 53, 59, 67, 71, 73, 79, 83, 97, 113, 131, 137, 139, 167, 173, 179, 197, 223, 229, 233, 239, 271, 283, 293, 311, 313, 317, 331, 337, 347, 353, 359, 367, 373, 379, 383, 397, 431, 433, 439, 443, 467, 479, 523, 547, 571 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Repeatedly removing a digit from either the left or right produces only primes. There are 149677 terms in this sequence, ending with 8939662423123592347173339993799. The number of n-digit terms is A298048(n). - Jon E. Schoenfield, Jan 28 2022 LINKS T. D. Noe, Table of n, a(n) for n = 1..10000 I. O. Angell and H. J. Godwin, On Truncatable Primes, Math. Comput. 31, 265-267, 1977. T. D. Noe, Plot of all terms Carlos Rivera, Puzzle 2: Prime Strings, The Prime Puzzles and Problems Connection. Daniel Starodubtsev, Full sequence Eric Weisstein, MathWorld: Truncatable Prime Index entries for sequences related to truncatable primes EXAMPLE 139 is here because (removing 9 from the right) 13 is prime and (removing 1 from the left) 3 is prime. MATHEMATICA Clear[s]; s={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; Do[t=Join[t, s[i]], {i, n}]; t PROG (Python) from sympy import isprime def agen(): primes = [2, 3, 5, 7] while len(primes) > 0: yield from primes cands = set(int(d+str(p)) for p in primes for d in "123456789") cands |= set(int(str(p)+d) for p in primes for d in "1379") primes = sorted(c for c in cands if isprime(c)) afull = [an for an in agen()] print(afull[:60]) # Michael S. Branicky, Aug 04 2022 CROSSREFS Cf. A024770 (right-truncatable primes), A024785 (left-truncatable primes), A077390 (left-and-right truncatable primes), A080608. Cf. A298048 (number of n-digit terms). Sequence in context: A080608 A305352 A347864 * A216578 A094317 A074834 Adjacent sequences: A137809 A137810 A137811 * A137813 A137814 A137815 KEYWORD base,fini,nonn AUTHOR T. D. Noe, Feb 11 2008 STATUS approved

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Last modified June 3 14:25 EDT 2023. Contains 363116 sequences. (Running on oeis4.)