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 A125590 Largest n-digit base-10 deletable prime. 1
 7, 97, 997, 9973, 99929, 999907, 9999907, 99999307, 999996671, 9999996073, 99999966307, 999999908773, 9999999710639, 99999999697769, 999999997160639, 9999999996977699, 99999999980803477, 999999999961861807, 9999999999961861807, 99999999999807429133 (list; graph; refs; listen; history; text; internal format)
 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. "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. REFERENCES C. Caldwell, Truncatable primes, J. Recreational Math., 19:1 (1987) 30-33. [Discusses left truncatable primes, right truncatable primes and deletable primes.] LINKS Table of n, a(n) for n=1..20. I. O. Angell and H. J. Godwin, On Truncatable Primes, Math. Comput. 31, 265-267, 1977. C. Caldwell, Deletable primes Prime Curios, A 300-digit example Carlos Rivera, Puzzle 138: Deletable Primes, Prime Puzzles and Problems Connection. [Includes a 500-digit example] Index entries for sequences related to truncatable primes EXAMPLE 99929 -> 9929 -> 929 -> 29 -> 2. MATHEMATICA b = 10; a = {7}; d = {2, 3, 5, 7}; For[n = 2, n <= 5, n++, p = Select[Range[b^(n - 1), b^n - 1], PrimeQ[#] &]; 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]]]; Break[]]]]; AppendTo[a, Last[d]]]; a (* Robert Price, Nov 13 2018 *) PROG (Python) from sympy import isprime, prevprime from functools import cache @cache def deletable_prime(n): if not isprime(n): return False if n < 10: return True s = str(n) si = (s[:i]+s[i+1:] for i in range(len(s))) return any(t[0] != '0' and deletable_prime(int(t)) for t in si) def a(n): p = prevprime(10**n) while not deletable_prime(p): p = prevprime(p) return p print([a(n) for n in range(1, 15)]) # Michael S. Branicky, Jan 13 2022 CROSSREFS Cf. A080608, A096243, A096246, A125589. Sequence in context: A178007 A241206 A127892 * A068694 A158579 A003618 Adjacent sequences: A125587 A125588 A125589 * A125591 A125592 A125593 KEYWORD nonn,base AUTHOR N. J. A. Sloane, Jan 07 2007 EXTENSIONS a(6)-a(8) from Michael Kleber, Jan 08 2007 a(9)-a(16) from Joshua Zucker, May 11 2007 a(17)-a(20) from Michael S. Branicky, Jan 13 2022 STATUS approved

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Last modified August 5 17:52 EDT 2024. Contains 374954 sequences. (Running on oeis4.)