A076730 Maximum number of (distinct) primes that an n-digit number may shelter (i.e., primes contained among all digital substrings' permutations).

1, 4, 11, 31, 106, 402, 1953, 10542, 64905, 362451, 2970505

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

Table of n, a(n) for n=1..11.

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
(Python) # see linked program in A076449

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 A353425 A155962

Adjacent sequences: A076727 A076728 A076729 * A076731 A076732 A076733

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