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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 (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..16.

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

Prime Puzzles, Puzzle 138: Deletable Primes [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 *)

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,more

AUTHOR

N. J. A. Sloane, Jan 07 2007

EXTENSIONS

a(6)-a(8) from Michael Kleber, Jan 08 2007

Extended through a(17) by Joshua Zucker

STATUS

approved

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Last modified February 20 23:24 EST 2019. Contains 320362 sequences. (Running on oeis4.)