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A096236
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Number of n-digit base-3 deletable primes.
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2
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1, 2, 4, 7, 13, 24, 38, 72, 122, 226, 400, 684, 1246, 2381, 4384, 8330, 15839, 30617, 58764, 113987, 221994, 434498, 852036, 1673320, 3296641, 6509179
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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MATHEMATICA
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b = 3; a = {1}; d = {2};
For[n = 2, n <= 10, 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]];
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PROG
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(Python)
from sympy import isprime
from sympy.ntheory.digits import digits
def ok(n, prevset, base=3):
if not isprime(n): return False
s = "".join(str(d) for d in digits(n, base)[1:])
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, base = {2}, set(), 3
print(len(s), end=", ")
for n in range(2, terms+1):
for i in range(base**(n-1), base**n):
if ok(i, s):
snxt.add(i)
s, snxt = snxt, set()
print(len(s), end=", ")
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CROSSREFS
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KEYWORD
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nonn,more,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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