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%I #12 Nov 25 2024 08:40:24
%S 1,2,3,5,7,9,11,13,17,19,21,23,27,29,31,33,37,39,51,53,57,59,71,73,77,
%T 79,91,93,97,99,111,113,117,119,131,133,137,139,171,173,177,179,191,
%U 193,197,199,211,213,217,219,231,233,237,239,271,273,277,279,291,293,297
%N Numbers n with the property that if m is formed from n by dropping any number (possibly zero) of initial or final digits then there is a prime ending with m.
%C Are all the numbers represented by the regular expressions ([2|5])[1|3|7|9]+ in this sequence?
%C Yes. In fact the members of this sequence are just those represented by the regular expression [123579][1379]* and hence the sequence is 10-automatic. - _Charles R Greathouse IV_, Jan 02 2013
%H <a href="/index/Ar#10-automatic">Index entries for 10-automatic sequences</a>.
%F a(n) ≍ n^k where k = log 10/log 4 = 1.6609.... - _Charles R Greathouse IV_, Nov 25 2024
%e 199 is in the sequence since there are primes that end with 199, 19, 99, 1 and 9 (namely 199, 19, 199, 11 and 19). 41 is not in the sequence since no primes ends with 4.
%o (Perl) for($n=1;$n<=999;$n++){
%o print "$i, " if($n =~ /^[123579][1379]*$/)
%o } # _Charles R Greathouse IV_, Jan 02 2013
%o (PARI) is(n)=my(d=digits(n)); (d[1]%2 || d[1]==2) && (#d<2 || vecsort(concat([1,3,7,9],d[2..#d]),,8)==[1,3,7,9]) \\ _Charles R Greathouse IV_, Jan 02 2013
%Y Cf. A004022, A004023.
%K base,nonn,easy
%O 1,2
%A Friedrich Laher (fritzl7(AT)netscape.net), Nov 27 2001
%E Corrected and extended by _Frank Ellermann_, Dec 10 2001
%E Corrected by _T. D. Noe_, Nov 01 2006
%E a(31) from _Charles R Greathouse IV_, Jan 02 2013