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

Author

Friedrich Laher (fritzl7(AT)netscape.net), Nov 27 2001

Keywords

• base
• nonn
• easy

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

Examples

			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.
		

Links

• Index entries for 10-automatic sequences.

Crossrefs

Cf. A004022, A004023.

Programs

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

Perl

for($n=1;$n<=999;$n++){
  print "$i, " if($n =~ /^[123579][1379]*$/)
} # Charles R Greathouse IV, Jan 02 2013

Formula

a(n) ≍ n^k where k = log 10/log 4 = 1.6609.... - Charles R Greathouse IV, Nov 25 2024

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