A294267 Largest k such that there exists a decimal string of length n containing each of the first k primes as a subsequence.

1, 2, 3, 4, 4, 7, 12, 17, 20, 22, 25, 29, 46, 58, 63, 85

Offset

1,2

Links

Table of n, a(n) for n=1..16.

Carlos Rivera, Puzzle 896: Optimal packing of a set of integers

Example

For n=1, "2" contains the first 1 prime as a subsequence, so a(1)=1.
For n=2, "23" contains each of the first 2 primes as a subsequence, so a(2)=2.
For n=3, "235" contains each of the first 3 primes as a subsequence, so a(3)=3.
For n=4, "2357" contains each of the first 4 primes as a subsequence, so a(4)=4.
For n=5, we cannot add any new primes as the 5th prime (11) requires two extra digits, so a(5)=a(4)=4.
For n=6, "112357" contains each of the first 7 primes (2 to 17) as a subsequence, so a(6)=7.
For n=7, "1231579" contains each of the first 12 primes (2 to 37) as a subsequence, so a(7)=12.

Crossrefs

Smallest strings are in A294268.

Sequence in context: A364675 A241315 A136330 * A301763 A236129 A240219

Adjacent sequences: A294264 A294265 A294266 * A294268 A294269 A294270

Keyword

nonn,base,more

Author

Dmitry Kamenetsky, Feb 11 2018

Status

approved