

A125590


Largest ndigit base10 deletable prime.


1



7, 97, 997, 9973, 99929, 999907, 9999907, 99999307, 999996671, 9999996073, 99999966307, 999999908773, 9999999710639, 99999999697769, 999999997160639, 9999999996977699
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OFFSET

1,1


COMMENTS

A prime p is a baseb 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) 3033. [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, 265267, 1977.
C. Caldwell, Deletable primes
Prime Curios, A 300digit example
Prime Puzzles, Puzzle 138: Deletable Primes [Includes a 500digit 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



