A321701 Primes that are not base-5 deletable primes (written in base 10).

5, 29, 31, 41, 43, 83, 101, 109, 127, 131, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 199, 211, 223, 229, 233, 241, 251, 257, 277, 281, 283, 293, 313, 331, 349, 383, 401, 409, 419, 421, 431, 433, 443, 457, 461, 463, 467, 491, 499, 509, 521, 541, 577, 587, 593, 599

Offset: 1

Author

Robert Price, Nov 17 2018

Keywords

• nonn
• base
• easy

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 A321700.

Links

• Robert Price, Table of n, a(n) for n = 1..31550

Crossrefs

Cf. A080608, A080603, A096235-A096246, A321657.

Programs

Mathematica

b = 5; 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 *)