A213306 Minimal prime with n nonprime substrings (Version 2: substrings with leading zeros are counted as nonprime if the corresponding number is > 0).

2, 13, 11, 103, 101, 149, 1009, 1021, 1049, 1481, 10039, 10069, 10169, 11681, 14669, 100109, 100189, 100169, 101681, 104681, 146669, 1000669, 1001041, 1001081, 1004669, 1014469, 1046849, 1468469, 10001081, 10004669, 10010851

Offset

0,1

Links

Hieronymus Fischer, Table of n, a(n) for n = 0..100

Formula

a(n) > 10^floor((sqrt(8*n+1)-1)/2), for n>2.

a(n) >= A213303(n).

a(n) <= A213307(n).

Example

a(0) = 2, since 2 is the least number with zero nonprime substrings.
a(1) = 13, since 13 has 1 nonprime substring (=’1’).
a(2) = 11, since 11 is the least number with 2 nonprime substrings (= 2 times ‘1’).
a(3) = 103, since 103 is the least number with 3 nonprime substrings, these are ‘1’ and ‘10’ and ‘03’ (‘0’ is not a valid substring in version 2).

Crossrefs

Cf. A019546, A035232, A039996, A046034, A069489, A085823, A211681, A211682, A211684, A211685.

Cf. A035244, A079307, A213300 - A213321.

Sequence in context: A157480 A342953 A355896 * A213307 A213305 A002591

Adjacent sequences: A213303 A213304 A213305 * A213307 A213308 A213309

Keyword

nonn,base

Author

Hieronymus Fischer, Aug 26 2012

Status

approved