A333965 Numbers k such that k * A171744(k) increases to a record.

1, 2, 5, 6, 8, 12, 14, 16, 18, 20, 25, 27, 32, 43, 45, 46, 52, 58, 70, 71, 77, 81, 91, 105, 109, 149, 158, 176, 240, 247, 297, 303, 401, 421, 431, 531, 536, 542, 543, 608, 617, 622, 640, 643, 667, 677, 685, 713, 720, 748, 751, 1028, 1085, 1203, 1282, 1320, 1466, 1600

Offset: 1

Author

David A. Corneth, Aug 14 2020

Keywords

• nonn
• base

Examples

			6 is in the sequence as A171744(6) = 22 and 6*22 = 132. This is a record; no n less than 6 produces a product of at least 132.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..1064

Crossrefs

Cf. A171744.

Programs

Maple

f:= proc(p) local t,k;
    t:= 1;
    for k from 1 do
      t:= t*p;
      if nops(convert(convert(t,base,10),set))=10 then return k fi;
    od
end proc:
R:= NULL: m:= 0: p:= 1: count:= 0:
for k from 1 while count < 100 do
  p:= nextprime(p);
  v:= k*f(p);
  if v > m then
    R:= R,k;
    m:= v;
    count:= count+1
  fi
od:
R; # Robert Israel, Aug 05 2024

Mathematica

With[{s = Array[Block[{p = Prime@ #, k = 1}, While[Min@ DigitCount[p^k] == 0, k++]; k #] &, 1600]}, Map[FirstPosition[s, #][[1]] &, Union@ FoldList[Max, s]]] (* Michael De Vlieger, Aug 21 2020 *)

PARI

f(n) = {my(k=1, p=prime(n)); while(#Set(digits(p^k))<10, k++); k; } \\ A171744
lista(nn) = {my(m=0, x); for (n=1, nn, x = n*f(n); if (x >m, m = x; print1(n, ", ")););} \\ Michel Marcus, Jan 26 2021