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, 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

Links

Table of n, a(n) for n=1..61.

Index entries for 10-automatic 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: A328336 A337694 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