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A385126 Hereditarily evil prime powers: numbers of the form p^k where p is prime and p^j is evil for 1 <= j <= k.

%I A385126 #9 Jun 25 2025 00:44:59
%S A385126 3,5,9,17,23,27,29,43,53,71,83,89,101,113,139,149,163,197,257,263,269,
%T A385126 277,281,293,311,317,337,347,349,353,359,373,383,389,401,449,461,467,
%U A385126 479,503,509,523,547,571,593,599,619,643,673,683,691,739,751,773,797,811,821,839,853,857,863,881
%N A385126 Hereditarily evil prime powers: numbers of the form p^k where p is prime and p^j is evil for 1 <= j <= k.
%H A385126 Robert Israel, <a href="/A385126/b385126.txt">Table of n, a(n) for n = 1..10000</a>
%e A385126 a(6) = 27 is a term because 3, 9 and 27 are all evil.
%e A385126 The first term that is a fourth power is 277^4 = 5887339441.
%e A385126 The first term that is a fifth power is 317^5 = 3201078401357.
%p A385126 isevil:= proc(n) convert(convert(n,base,2),`+`)::even end proc:
%p A385126 M:= 1000: # for terms <= M
%p A385126 R:= NULL:
%p A385126 p:= 1:
%p A385126 do
%p A385126   p:= nextprime(p);
%p A385126   if p > M then break fi;
%p A385126   for k from 1 do
%p A385126     z:= p^k;
%p A385126     if z > M then break fi;
%p A385126     if isevil(z) then R:= R, z
%p A385126     else break
%p A385126     fi
%p A385126   od
%p A385126 od:
%p A385126 sort([R]);
%Y A385126 Cf. A001969.
%Y A385126 Contains A027699.
%K A385126 nonn,base
%O A385126 1,1
%A A385126 _Robert Israel_, Jun 18 2025