A256523 Numbers m such that m, m^2 and m^3 have identical initial digits in decimal representation.

0, 1, 10, 11, 12, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 966, 967, 968, 969, 970, 971, 972, 973, 974, 975, 976, 977, 978, 979, 980, 981, 982, 983, 984, 985

Offset: 1

Author

Reinhard Zumkeller, Apr 01 2015

Keywords

• nonn
• base

Comments

Intersection of A089951 and A144582.

From Jianing Song, Dec 26 2022: (Start)

For k > 0, write k = s * 10^t, 1 <= s < 10, then k is a term if and only if s is in [1, 2^(1/3)) U (30^(2/3), 10).

Except for 0, terms of A144582 that start with 1 or 9. (End)

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000030, A089951, A144582, A000290, A000578, A002993, A002994.

Programs

Haskell

a256523 n = a256523_list !! (n-1)
a256523_list = [x | x <- [0..], let i = a000030 x,
                    a000030 (x ^ 2) == i, a000030 (x ^ 3) == i]

Mathematica

Select[Range[0,1000],Length[Union[(IntegerDigits/@(#^Range[3]))[[;;,1]]]]==1&] (* Harvey P. Dale, Dec 17 2024 *)

PARI

initial(n)=digits(n)[1]
is(n)=if(n==0, return(1)); my(k=initial(n)); initial(n^2)==k && initial(n^3)==k \\ Charles R Greathouse IV, May 13 2015

Formula

A000030(a(n)) = A002993(a(n)) = A000030(A000290(a(n))) = A002994(a(n)) = A000030(A000578(a(n))).