A322443 -id:A322443 - cp's OEIS frontend

A322444 Primes that are not base-8 deletable primes (written in base 10).

71, 73, 79, 97, 103, 113, 127, 149, 173, 193, 227, 241, 257, 263, 271, 281, 283, 307, 311, 313, 409, 419, 433, 439, 449, 457, 463, 487, 503, 521, 569, 577, 587, 593, 599, 607, 617, 631, 641, 647, 653, 661, 673, 701, 727, 733, 739, 743, 757, 769, 823, 827, 839, 881, 887, 907, 911, 919, 929

Offset: 1

Robert Price, Dec 08 2018

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 A322443 .

Robert Price, Table of n, a(n) for n = 1..660

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

b = 8; 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 08 2018 *)

A096241 Number of n-digit base-8 deletable primes.

Original entry on oeis.org

4, 14, 50, 238, 1123, 5792, 30598, 166056, 927639, 5308458, 30984757

Offset: 1

Michael Kleber, Feb 28 2003

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. "Digit" means digit in base b.

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.

Cf. A080608, A080603, A096235-A096246, A322443.

b = 8; a = {4}; d = {2, 3, 5, 7};
For[n = 2, n <= 5, n++,
  p = Select[Range[b^(n - 1), b^n - 1], PrimeQ[#] &];
  ct = 0;
  For[i = 1, i <= Length[p], i++,
   c = IntegerDigits[p[[i]], b];
   For[j = 1, j <= n, j++,
    t = Delete[c, j];
    If[t[[1]] == 0, Continue[]];
    If[MemberQ[d, FromDigits[t, b]], AppendTo[d, p[[i]]]; ct++;
     Break[]]]];
  AppendTo[a, ct]];
a (* Robert Price, Nov 13 2018 *)

from sympy import isprime
def ok(n, prevset, base=8):
    if not isprime(n): return False
    s = oct(n)[2:]
    si = (s[:i]+s[i+1:] for i in range(len(s)))
    return any(t[0] != '0' and int(t, base) in prevset for t in si)
def afind(terms):
    s, snxt = {2, 3, 5, 7}, set()
    print(len(s), end=", ")
    for n in range(2, terms+1):
        for i in range(8**(n-1), 8**n):
            if ok(i, s):
                snxt.add(i)
        s, snxt = snxt, set()
        print(len(s), end=", ")
afind(7) # Michael S. Branicky, Jan 14 2022

a(6)-a(10) from Ryan Propper, Jul 19 2005

a(11) from D. S. McNeil, Dec 08 2009

cp's OEIS Frontend

A322444 Primes that are not base-8 deletable primes (written in base 10).

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