A213305 Minimal prime with n nonprime substrings (Version 1: substrings with leading zeros are considered to be nonprime).

2, 13, 11, 127, 103, 101, 1013, 1019, 1021, 1009, 10177, 10037, 10067, 10007, 10009, 100237, 100271, 100153, 100043, 100003, 100049, 1001173, 1000313, 1000037, 1000033, 1000039, 1000003, 1000081, 10000379, 10001237, 10000223

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>0.

a(m(m+1)/2) > 10^m, m>0.

a(n) >= A213302(n).

Example

a(0) = 2, since 2 is the least prime with zero nonprime substrings.
a(1) = 13, since 13 is the least prime with exactly 1 (“1”) nonprime substrings.
a(2) = 11, since 11 is the least prime with exactly 2 (“1” and “1”) nonprime substrings.

Crossrefs

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

Cf. A035244, A079307, A213300 - A213321.

Sequence in context: A355896 A213306 A213307 * A002591 A037055 A065584

Adjacent sequences: A213302 A213303 A213304 * A213306 A213307 A213308

Keyword

nonn,base

Author

Hieronymus Fischer, Aug 26 2012

Status

approved