A096237 - OEIS

%I #19 Jan 17 2022 11:40:41

%S 2,3,9,26,75,213,615,1853,5854,18664,61248,205300,698575,2409598,

%T 8408050,29657194

%N Number of n-digit base-4 deletable primes.

%C 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.

%C 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.

%t b = 4; a = {2}; d = {2, 3};

%t For[n = 2, n <= 8, n++,

%t   p = Select[Range[b^(n - 1), b^n - 1], PrimeQ[#] &];

%t   ct = 0;

%t   For[i = 1, i <= Length[p], i++,

%t    c = IntegerDigits[p[[i]], b];

%t    For[j = 1, j <= n, j++,

%t     t = Delete[c, j];

%t     If[t[[1]] == 0, Continue[]];

%t     If[MemberQ[d, FromDigits[t, b]], AppendTo[d, p[[i]]]; ct++;

%t      Break[]]]];

%t   AppendTo[a, ct]];

%t a (* _Robert Price_, Nov 12 2018 *)

%o (Python)

%o from sympy import isprime

%o from sympy.ntheory.digits import digits

%o def ok(n, prevset, base=4):

%o     if not isprime(n): return False

%o     s = "".join(str(d) for d in digits(n, base)[1:])

%o     si = (s[:i]+s[i+1:] for i in range(len(s)))

%o     return any(t[0] != '0' and int(t, base) in prevset for t in si)

%o def afind(terms):

%o     alst = [2]

%o     s, snxt, base = {2, 3}, set(), 4

%o     print(len(s), end=", ")

%o     for n in range(2, terms+1):

%o         for i in range(base**(n-1), base**n):

%o             if ok(i, s):

%o                 snxt.add(i)

%o         s, snxt = snxt, set()

%o         print(len(s), end=", ")

%o afind(10) # _Michael S. Branicky_, Jan 17 2022

%Y Cf. A080608, A080603, A096235-A096246.

%K nonn,base,more

%O 1,1

%A _Michael Kleber_, Feb 28 2003

%E a(6)-a(15) from _Ryan Propper_, Jul 19 2005

%E a(16) from _Michael S. Branicky_, Jan 17 2022