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

1,2

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).

Links

Table of n, a(n) for n=1..50.

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

Crossrefs

Sequence in context: A090516 A090515 A075309 * A052054 A046447 A087244

Adjacent sequences: A175028 A175029 A175030 * A175032 A175033 A175034

Keyword

base,nonn

Author

Zak Seidov, Nov 06 2009

Status

approved