A320587 Primes that are not Base-3 deletable primes (written in base 10).

3, 13, 31, 37, 41, 43, 67, 79, 97, 103, 109, 113, 127, 131, 139, 149, 151, 157, 163, 193, 199, 211, 227, 229, 239, 241, 257, 271, 277, 281, 283, 293, 307, 311, 313, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 433, 439, 443

Offset

1,1

Comments

A prime p is a base-b deletable prime if when written in base b it has the property that removing some digit leaves either the empty string or another deletable prime.

Deleting a digit cannot leave any leading zeros in the new string. For example, deleting the 2 in 2003 to obtain 003 is not allowed.

Complement of all primes and A319596.

Links

Robert Price, Table of n, a(n) for n = 1..906

Mathematica

b = 3; d = {};
p = Select[Range[2, 10000], PrimeQ[#] &];
For[i = 1, i <= Length[p], i++,
  c = IntegerDigits[p[[i]], b];
  If[Length[c] == 1, AppendTo[d, p[[i]]]; Continue[]];
  For[j = 1, j <= Length[c], j++,
   t = Delete[c, j];
   If[t[[1]] == 0, Continue[]];
If[MemberQ[d, FromDigits[t, b]], AppendTo[d, p[[i]]]; Break[]]]]; Complement[Table[Prime[n], {n, PrimePi[Last[d]]}], d] (* Robert Price, Dec 06 2018 *)

Crossrefs

Cf. A080608, A080603, A096235-A096246.

Sequence in context: A273337 A273769 A097955 * A077717 A235265 A347988

Adjacent sequences: A320584 A320585 A320586 * A320588 A320589 A320590

Keyword

nonn,base,easy

Author

Robert Price, Nov 14 2018

Extensions

Added the term 3. As pointed out by Kevin Ryde, there is no need to "seed" the list using base-2 assumptions. - Robert Price, Dec 06 2018

Status

approved