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

1,1

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. 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

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]

Crossrefs

Cf. A080608, A080603, A096235-A096246.

Sequence in context: A062579 A134076 A258029 * A160961 A260805 A267781

Adjacent sequences: A321593 A321594 A321595 * A321597 A321598 A321599

Keyword

nonn,base,easy

Author

Robert Price, Nov 14 2018

Status

approved