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A020994 Primes that are both left-truncatable and right-truncatable. 18

%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

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Last modified March 28 07:33 EDT 2024. Contains 371235 sequences. (Running on oeis4.)