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 A076730 Maximum number of (distinct) primes that an n-digit number may shelter (i.e., primes contained among all digital substrings' permutations). 3
 1, 4, 11, 31, 106, 402, 1953, 10542, 64905, 362451, 2970505 (list; graph; refs; listen; history; text; internal format)
 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 a(n) = A076497(k) for k such that A072857(k) = A134596(n). - M. F. Hasler, Oct 15 2019 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 CROSSREFS Cf. A072857, A076449, A076497, A134596 (largest n-digit primeval number). Cf. A075053 (a variant of A039993), A134597 (= max A075053(1..10^n-1)). Sequence in context: A296572 A176573 A134597 * A084757 A155962 A027153 Adjacent sequences:  A076727 A076728 A076729 * A076731 A076732 A076733 KEYWORD hard,more,base,nonn,changed 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

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Last modified October 18 10:24 EDT 2019. Contains 328146 sequences. (Running on oeis4.)