A065853 - OEIS

A065853

Let u be any string of 4 digits from {0,...,n-1}; let f(u) = number of distinct primes, not beginning with 0, formed by permuting the digits of u to a base-n number; then a(n) = max_u f(u).

2, 4, 6, 7, 8, 15, 11, 11, 11, 15, 15, 19, 11, 14, 15, 14, 11, 16, 13, 18, 14, 14, 14, 16, 13, 16, 15, 17, 13, 16, 14, 15, 17, 16, 15, 16, 14, 17, 14, 17, 16, 17, 14, 16, 15, 15, 14, 17, 17, 16, 16, 16, 15, 18, 16, 17, 14, 15, 14, 16, 15, 15, 16, 16, 17, 17, 13, 17, 15, 17, 13

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OFFSET

2,1

LINKS

Table of n, a(n) for n=2..72.

EXAMPLE

a(2)=2 because 1101 and 1011 are primes and there are no three 4-digit primes with the same number of ones in base 2.

MATHEMATICA

c[x_, n_] :=

Module[{},

Length[Select[Permutations[x],

First[#] != 0 && PrimeQ[FromDigits[#, n]] &]]];

A065853[n_] := Module[{i},

Return[ Max[Map[c[#, n] &,

DeleteDuplicatesBy[Tuples[Range[0, n - 1], 4],

Table[Count[#, i], {i, 0, n - 1}] &]]]]];

Table[A065853[n], {n, 2, 20}] (* Robert Price, Mar 30 2019 *)

CROSSREFS

Cf. A065843, A065844, A065845, A065846, A065847, A065848, A065849, A065850, A065851, A065852.

Sequence in context: A096750 A088458 A177866 * A048284 A026516 A289012

Adjacent sequences: A065850 A065851 A065852 * A065854 A065855 A065856

KEYWORD

base,nonn

AUTHOR

Sascha Kurz, Nov 24 2001

EXTENSIONS

Definition corrected by David A. Corneth, Apr 23 2016

STATUS

approved