

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
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OFFSET

1,2


COMMENTS

Are all the numbers represented by the regular expressions ([25])[1379]+ 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 10automatic.  Charles R Greathouse IV, Jan 02 2013


LINKS

Table of n, a(n) for n=1..61.
Index entries for 10automatic sequences.


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

Cf. A004022, A004023.
Sequence in context: A305078 A328336 A305103 * A316428 A277702 A279516
Adjacent sequences: A065517 A065518 A065519 * A065521 A065522 A065523


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



