|
|
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
|
|
|
|