A393306 a(n) is the greatest number k that contains, in base n, every digit exactly once, and such that k/(n-1) (if n is even) or 2*k/(n-1) (if n is odd) is prime.

2, 19, 201, 2902, 44185, 799899, 16434817, 381367036, 9876541023, 282458540465, 8842413667417, 300771807236682, 11046255305795333, 435659737878916201, 18364758544492069665, 824008854613343260616, 39210261334551566850727, 1972313422155189164329713, 104567135734072022160160883

Offset

2,1

Comments

Every number that contains, in base n, every digit once is divisible by n-1 (if n is even) or (n-1)/2 (if n is odd).

Conjecture: a(n) exists for all n.

Links

Robert Israel, Table of n, a(n) for n = 2..385

Example

a(4) = 201 because 201 = 3021_4 contains all digits 0 to 3 once in base 4, 201/(4-1) = 67 is prime, and no larger number works.

Maple

f:= proc(n) local b, p, x, i; uses combinat;
      b:= `if`(n::even, n-1, (n-1)/2);
      p:= lastperm(n);
      do
        x:= add((p[i]-1)*n^(n-i), i=1..n);
        if isprime(x/b) then return x fi;
        p:= prevperm(p);
        if p = FAIL then return -1 fi
      od;
end proc:
map(f, [$2..30]);

Crossrefs

Cf. A380386.

Sequence in context: A037071 A397538 A126039 * A349256 A091852 A210986

Adjacent sequences: A393303 A393304 A393305 * A393307 A393308 A393309

Keyword

nonn,base

Author

Robert Israel, Feb 10 2026

Status

approved