A175031 Sequence of increasing positive perfect powers such that neighboring digits in the sequence are distinct.

1, 4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 81, 216, 243, 256, 289, 324, 343, 484, 512, 529, 576, 729, 784, 841, 961, 2025, 2048, 2187, 2197, 2304, 2401, 2601, 2704, 2809, 2916, 3025, 3125, 3136, 3249, 3481, 3721, 3969, 4096, 4356, 4624, 5041, 5184, 5329, 5476

Offset: 1

Author

Zak Seidov, Nov 06 2009

Keywords

• base
• nonn

Comments

Subsequence of A090516 (Perfect powers (at least a square) in which neighboring digits are distinct.) which itself is subsequence of A001597 ( Perfect powers: m^k where m is an integer and k >= 2) which itself is Subsequence of A000027 (natural numbers).

Programs

Mathematica

m=26000;a=1;A001597=Union[Join[{a},Flatten[Table[n^i,{n,2,Sqrt[m]},{i,2,Log[n,m]}]]]]; A090516=Select[A001597,Max[Length/@Split[IntegerDigits[ # ]]]==1&]; S={1};ia1={a};Do[si=A090516[[i]];If[IntegerDigits[si][[1]]!=ia1,AppendTo[S,si];ia1=IntegerDigits[si][[ -1]]],{i,2,Length[se1]}]; S