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%I #23 Oct 16 2019 06:20:06
%S 1,4,11,31,106,402,1953
%N a(n) gives the maximal value of A075053(m) for any n-digit number m.
%C In A075053(m), the primes obtained as permutations of digits of m are counted several times if they can be obtained in several different ways. See sequence A076730 which uses A039993 instead, i.e., counting only different primes. - _M. F. Hasler_, Mar 11 2014
%C The original data given for n = 3, 4, 5 was erroneously A007526(n). - Up to n = 6, a(n) = A076730(n), but the two will differ not later than for n = 10, where A134596(10) = 1123456789 gives a(10) >= 398100 = A075053(1123456789) > A039993(1123456789) = 362451 = A076730(10). The difference arises because each prime containing a single '1' will be counted twice by A075053, but only once by A039993. - _M. F. Hasler_, Oct 14 2019
%H M. Keith, <a href="http://www.cadaeic.net/primeval.htm">Integers containing many embedded primes</a>
%F a(n) <= A007526(n), with equality iff n <= 2. [Keith]
%F a(n) = max { A075053(m); 10^(n-1) <= m < 10^n } >= A076730(n) = max { A039993(m); 10^(n-1) <= m < 10^n }. - _M. F. Hasler_, Mar 11 2014
%e From _M. F. Hasler_, Oct 14 2019: (Start)
%e a(2) = 4 = A075053(37), because from 37 one can obtain the primes {3, 7, 37, 73}, and there is obviously no 2-digit number which could give more primes.
%e a(3) = 11 = A075053(137), because from 137 one can obtain the primes {3, 7, 13, 17, 31, 37, 71, 73, 137, 173, 317}, and no 3-digit number yields more.
%e a(4) = 31 = A075053(1379), because from 1379 one can obtain the 31 primes {3, 7, 13, 17, 19, 31, 37, 71, 73, 79, 97, 137, 139, 173, 179, 193, 197, 317, 379, 397, 719, 739, 937, 971, 1973, 3719, 3917, 7193, 9137, 9173, 9371}, and no 4-digit number yields more.
%e a(5) = 106 = A075053(13679). a(6) = 402 = A075053(123479).
%e a(7) = 1953 = A075053(1234679). (End)
%o (PARI) A134597(n)={my(m=0);forvec(D=vector(n,i,[0,9]), vecsum(D)%3||next;m=max(A075053(fromdigits(D),D),m),1);m} \\ _M. F. Hasler_, Oct 14 2019
%Y Cf. A075053, A039993, A134596.
%Y Cf. A239196 for record indices of A075053, A239197 for associated record values.
%K nonn,base,more
%O 1,2
%A _N. J. A. Sloane_, Jan 25 2008
%E Link fixed by _Charles R Greathouse IV_, Aug 13 2009
%E Definition corrected by _M. F. Hasler_, Mar 11 2014
%E Data corrected and extended by _M. F. Hasler_, Oct 14 2019
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