A213304 - OEIS

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A213304

Smallest number with n nonprime substrings (Version 3: substrings with leading zeros are counted as nonprime if the corresponding number is not a prime).

2, 1, 10, 14, 101, 104, 144, 1001, 1014, 1044, 1444, 10010, 10014, 10144, 10444, 14444, 100120, 100104, 100144, 101444, 104444, 144444, 1000144, 1001040, 1001044, 1001444, 1014444, 1044444, 1444444, 10001044, 10001444, 10010404, 10010444, 10014444, 10144444, 10444444, 14444444, 100010404, 100010444, 100014444, 100104044, 100104444, 100144444, 101444444, 104444444, 144444444

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OFFSET

0,1

COMMENTS

The sequence is well defined since for each n >= 0 there is a number with n nonprime substrings.

Different from A213303, first difference is at a(16).

LINKS

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

FORMULA

a(m(m+1)/2) = (13*10^(m-1)-4)/9, m>0.

With b(n):=floor((sqrt(8*n-7)-1)/2):

a(n) > 10^b(n), for n>2, a(n) = 10^b(n) for n=1,2.