cp's OEIS Frontend

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

%I A333965 #29 Aug 06 2024 02:23:02
%S A333965 1,2,5,6,8,12,14,16,18,20,25,27,32,43,45,46,52,58,70,71,77,81,91,105,
%T A333965 109,149,158,176,240,247,297,303,401,421,431,531,536,542,543,608,617,
%U A333965 622,640,643,667,677,685,713,720,748,751,1028,1085,1203,1282,1320,1466,1600
%N A333965 Numbers k such that k * A171744(k) increases to a record.
%H A333965 Robert Israel, <a href="/A333965/b333965.txt">Table of n, a(n) for n = 1..1064</a>
%e A333965 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.
%p A333965 f:= proc(p) local t,k;
%p A333965     t:= 1;
%p A333965     for k from 1 do
%p A333965       t:= t*p;
%p A333965       if nops(convert(convert(t,base,10),set))=10 then return k fi;
%p A333965     od
%p A333965 end proc:
%p A333965 R:= NULL: m:= 0: p:= 1: count:= 0:
%p A333965 for k from 1 while count < 100 do
%p A333965   p:= nextprime(p);
%p A333965   v:= k*f(p);
%p A333965   if v > m then
%p A333965     R:= R,k;
%p A333965     m:= v;
%p A333965     count:= count+1
%p A333965   fi
%p A333965 od:
%p A333965 R; # _Robert Israel_, Aug 05 2024
%t A333965 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 *)
%o A333965 (PARI) f(n) = {my(k=1, p=prime(n)); while(#Set(digits(p^k))<10, k++); k; } \\ A171744
%o A333965 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
%Y A333965 Cf. A171744.
%K A333965 nonn,base
%O A333965 1,2
%A A333965 _David A. Corneth_, Aug 14 2020