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A065520
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.
1
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, 79, 91, 93, 97, 99, 111, 113, 117, 119, 131, 133, 137, 139, 171, 173, 177, 179, 191, 193, 197, 199, 211, 213, 217, 219, 231, 233, 237, 239, 271, 273, 277, 279, 291, 293, 297
OFFSET
1,2
COMMENTS
Are all the numbers represented by the regular expressions ([2|5])[1|3|7|9]+ in this sequence?
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
EXAMPLE
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.
PROG
(Perl) for($n=1; $n<=999; $n++){
print "$i, " if($n =~ /^[123579][1379]*$/)
} # Charles R Greathouse IV, Jan 02 2013
(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
CROSSREFS
Sequence in context: A328336 A337694 A305103 * A316428 A277702 A279516
KEYWORD
base,nonn,easy
AUTHOR
Friedrich Laher (fritzl7(AT)netscape.net), Nov 27 2001
EXTENSIONS
Corrected and extended by Frank Ellermann, Dec 10 2001
Corrected by T. D. Noe, Nov 01 2006
a(31) from Charles R Greathouse IV, Jan 02 2013
STATUS
approved