cp's OEIS Frontend

A308105 Numbers m such that m is greater than the sum of the k-th powers of its digits, where k is the number of digits of m.

%I A308105 #44 Sep 08 2022 08:46:21
%S A308105 10,11,12,13,20,21,22,23,24,30,31,32,33,34,35,40,41,42,43,44,45,50,51,
%T A308105 52,53,54,55,60,61,62,63,64,65,70,71,72,73,74,75,80,81,82,83,84,90,91,
%U A308105 92,93,100,101,102,103,104,110,111,112,113,114,120,121,122,123,124,130,131,132,133,134
%N A308105 Numbers m such that m is greater than the sum of the k-th powers of its digits, where k is the number of digits of m.
%C A308105 These integers are called "nombres résistants" on the French site Diophante.
%C A308105 There exists a smallest number M_0 such that every number >= M_0 is a term of this sequence. This integer has 60 digits: M_0 = 102 * 10^57. So 102 * 10^57 - 1 is not "résistant" (proof in the link).
%H A308105 Robert Israel, <a href="/A308105/b308105.txt">Table of n, a(n) for n = 1..10000</a>
%H A308105 Diophante, <a href="http://www.diophante.fr/problemes-par-themes/arithmetique-et-algebre/a3-nombres-remarquables/3969-a367-les-entiers-font-de-la-resistance">A367. Les entiers font de la résistance</a>, Oct. 2017 (in French).
%F A308105 Numbers m such that m - A101337(m) > 0.
%e A308105 34 - (3^2 + 4^2) = 9 so 34 is a term.
%e A308105 126 - (1^3 + 2^3 + 6^3) = -99 and 126 is not a term.
%p A308105 filter:= proc(n) local L,m,t;
%p A308105   L:= convert(n,base,10);
%p A308105   m:= nops(L);
%p A308105   n > add(t^m,t=L)
%p A308105 end proc:
%p A308105 select(filter, [$1..1000]); # _Robert Israel_, Jun 21 2019
%t A308105 Select[Range[140], # - Total[IntegerDigits[#]^IntegerLength[#]] > 0 &] (* _Michael De Vlieger_, Jun 09 2019 *)
%o A308105 (Magma) sol:=[];v:=[];digit:=[]; m:=1;
%o A308105 for u in [1..150] do
%o A308105         digit:=Intseq(u);
%o A308105              for i in [1..#digit] do v[i]:=digit[i]^#digit; end for;
%o A308105              if u-&+v gt 0 then sol[m]:=u; m:=m+1; end if;
%o A308105 end for;
%o A308105 sol; // _Marius A. Burtea_, May 13 2019
%o A308105 (PARI) isok(n) = { my(d=digits(n), nb=#d); n > sum(k=1, #d, d[k]^nb);} \\ _Michel Marcus_, May 19 2019
%Y A308105 Cf. A000027, A101337, A005188.
%K A308105 nonn,base
%O A308105 1,1
%A A308105 _Bernard Schott_, May 13 2019