Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #28 Jul 16 2022 11:48:42
%S 2,3,5,7,23,37,53,73,313,317,373,797,3137,3797,739397
%N Primes that are both left-truncatable and right-truncatable.
%C Two-sided primes: deleting any number of digits at left or at right, but not both, leaves a prime.
%C Primes in which every digit string containing the most significant digit or the least significant digit is prime. - _Amarnath Murthy_, Sep 24 2003
%C Intersection of A024785 and A024770. - _Robert Israel_, Mar 23 2015
%D David Wells, The Penguin Dictionary of Curious and Interesting Numbers, p. 178 (Rev. ed. 1997).
%H 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 Patrick De Geest, <a href="http://www.worldofnumbers.com/truncat.htm">The list of 4260 left-truncatable primes</a>
%H <a href="/index/Tri#tprime">Index entries for sequences related to truncatable primes</a>
%t tspQ[n_] := Module[{idn=IntegerDigits[n], l}, l=Length[idn]; Union[PrimeQ/@(FromDigits/@ Join[Table[Take[idn, i], {i, l}], Table[Take[idn, -i], {i, l}]])]=={True}] Select[Prime[Range[PrimePi[740000]]], tspQ]
%Y Cf. A033664, A024785, A032437, A024770, A052023, A052024, A052025, A050986, A050987, A254751, A254753.
%K nonn,fini,full,base
%O 1,1
%A Mario Velucchi (mathchess(AT)velucchi.it)
%E Corrected by _David W. Wilson_
%E Additional comments from _Harvey P. Dale_, Jul 10 2002