A321596 Primes that are not base-2 deletable primes (written in base 10).

17, 31, 41, 67, 71, 89, 97, 103, 113, 127, 131, 139, 181, 191, 193, 199, 223, 227, 233, 239, 241, 251, 257, 263, 269, 271, 283, 337, 353, 367, 373, 379, 383, 401, 409, 431, 433, 439, 443, 449, 463, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 571, 577

Offset: 1

Author

Robert Price, Nov 14 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. However, in base 2 we adopt the convention that 2 = 10 and 3 = 11 are deletable.

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 A096246.

Links

• Robert Price, Table of n, a(n) for n = 1..2351

Crossrefs

Cf. A080608, A080603, A096235-A096246.

Programs

Mathematica

d = {2, 3};
For[n = 3, n <= 15, n++,
  p = Select[Range[2^(n - 1), 2^n - 1], PrimeQ[#] &];
  For[i = 1, i <= Length[p], i++,
   c = IntegerDigits[p[[i]], 2];
   For[j = 1, j <= n, j++,
    t = Delete[c, j];
    If[t[[1]] == 0, Continue[]];
    If[MemberQ[d, FromDigits[t, 2]], AppendTo[d, p[[i]]];  Break[]]]]]; Complement[Table[Prime[n], {n, PrimePi[Last[d]]}], d]