OFFSET
1,2
COMMENTS
See sequence A134596 for the least numbers of given length which yields these maxima over n-digit indices for A039993. - M. F. Hasler, Mar 11 2014
By definition this is a subsequence of A076497. The term a(10) was incorrectly given as 398100 = A075053(1123456789), which double-counts each prime using only one digit '1'. But a(10) = A039993(1123456789) = A076497(80) = 362451. The values given for a(9) and a(11) were also incorrect, the latter probably for the same reason, and for a(9) probably due to double-counting of primes with leading zeros. - M. F. Hasler and David A. Corneth, Oct 15 2019
LINKS
M. Keith, Integers containing many embedded primes
W. Schneider, MATHEWS, Primeval Numbers
FORMULA
a(n) = A039993(A134596(n)) = max { A039993(m); m in A072857 and m < 10^n }. - M. F. Hasler, Mar 12 2014
EXAMPLE
We have a(3)=11, since among numbers 100 through 999, the smallest ones having 5, 6, 7, 8, 10, 11 embedded primes are respectively 107, 127, 113, 167, 179, 137 (the last of these being the first reaching the maximum number of 11 embedded primes, viz. 3, 7, 13, 17, 31, 37, 71, 73, 137, 173, 317).
PROG
(PARI) a(n, m=0)=for(k=10^(n-1), 10^n-1, A039993(k)>m&&m=A039993(k)); m \\ M. F. Hasler, Mar 09 2014
(Python) # see linked program in A076449
CROSSREFS
KEYWORD
hard,more,base,nonn
AUTHOR
Lekraj Beedassy, Nov 08 2002
EXTENSIONS
Link fixed by Charles R Greathouse IV, Aug 13 2009
a(6) from M. F. Hasler, Mar 09 2014
a(7)-a(11) from Robert G. Wilson v, Mar 11 2014
a(9)-a(11) corrected by M. F. Hasler, Oct 15 2019
STATUS
approved