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

3, 5, 9, 17, 23, 27, 29, 43, 53, 71, 83, 89, 101, 113, 139, 149, 163, 197, 257, 263, 269, 277, 281, 293, 311, 317, 337, 347, 349, 353, 359, 373, 383, 389, 401, 449, 461, 467, 479, 503, 509, 523, 547, 571, 593, 599, 619, 643, 673, 683, 691, 739, 751, 773, 797, 811, 821, 839, 853, 857, 863, 881

Offset: 1

Author

Robert Israel, Jun 18 2025

Keywords

• nonn
• base

Examples

			a(6) = 27 is a term because 3, 9 and 27 are all evil.
The first term that is a fourth power is 277^4 = 5887339441.
The first term that is a fifth power is 317^5 = 3201078401357.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001969.

Contains A027699.

Programs

Maple

isevil:= proc(n) convert(convert(n,base,2),`+`)::even end proc:
M:= 1000: # for terms <= M
R:= NULL:
p:= 1:
do
  p:= nextprime(p);
  if p > M then break fi;
  for k from 1 do
    z:= p^k;
    if z > M then break fi;
    if isevil(z) then R:= R, z
    else break
    fi
  od
od:
sort([R]);