A175053 Perfect powers (members of A001597) n where the next larger perfect power is not congruent mod 2 to n.

1, 8, 9, 16, 27, 36, 49, 64, 81, 100, 125, 144, 169, 216, 243, 256, 289, 324, 361, 400, 441, 512, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1024, 1089, 1156, 1225, 1296, 1369, 1444, 1521, 1600, 1681, 1764, 1849, 1936, 2025, 2116, 2209, 2304, 2401, 2500

Offset: 1

Author

Leroy Quet, Dec 08 2009

Keywords

• nonn

Examples

			125 (125 = 5^3) and 128 (128 = 2^7) are consecutive perfect powers. Since one of these is odd and the other is even, then 125 is in this sequence.
		

Links

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

Crossrefs

Cf. A001597, A175052

Programs

Maple

N:= 3000:
PP:= {1,seq(seq(i^k,i=2..floor(N^(1/k))),k=2..ilog2(N))}:
PP:= sort(convert(PP,list)):
PP[select(t -> PP[t+1] mod 2 <> PP[t] mod 2,[$1..nops(PP)-1])]; # Robert Israel, May 21 2025

Extensions

Extended by Ray Chandler, Dec 10 2009