A093140 -id:A093140 - cp's OEIS frontend

A093141 Expansion of (1-6x)/(1-10x).

1, 4, 40, 400, 4000, 40000, 400000, 4000000, 40000000, 400000000, 4000000000, 40000000000, 400000000000, 4000000000000, 40000000000000, 400000000000000, 4000000000000000, 40000000000000000, 400000000000000000, 4000000000000000000, 40000000000000000000, 400000000000000000000

Offset: 0

Paul Barry, Mar 24 2004

Partial sums are A093140. A convex combination of 10^n and 0^n.

Index entries for linear recurrences with constant coefficients, signature (10).

Cf. A093140.

Table[EulerPhi[10^n],{n,0,40}] (* Vladimir Joseph Stephan Orlovsky, Nov 10 2009 *)
Join[{1},NestList[10#&,4,20]] (* Harvey P. Dale, Apr 01 2018 *)

Vec((1-6*x)/(1-10*x) + O(x^30)) \\ Michel Marcus, Jan 17 2015

a(n) = 4*10^n/10 + 6*0^n/10.
a(n) = phi(10^n). - Paul Barry, Jul 02 2007
a(n) = 4*10^(n-1), n > 0. - Vincenzo Librandi, Aug 02 2010
From Elmo R. Oliveira, Aug 21 2024: (Start)
E.g.f.: (2*exp(10*x) + 3)/5.
a(n) = 10*a(n-1) for n > 1. (End)

a(19)-a(21) from Elmo R. Oliveira, Aug 21 2024

A362792 Numbers k such that 3k and 7k share the same set of digits.

Original entry on oeis.org

0, 45, 75, 423, 445, 450, 513, 750, 891, 1089, 1305, 2382, 2497, 4230, 4445, 4450, 4488, 4491, 4500, 4505, 4513, 4878, 5013, 5045, 5130, 5133, 5868, 7317, 7500, 7686, 8360, 8703, 8891, 8901, 8910, 8911, 8955, 8991, 9756, 9891, 10089, 10449, 10889, 10890, 10891

Offset: 1

Alexandru Petrescu, May 04 2023

The sequence is infinite because if k is a term, then 10*k is also a term.

Every number k of the form 44...45 (one of more 4's followed by 5, cf. A093140) is a term because 3*k = 133...35 and 7*k = 311...15.

			k = 75 is a term because 3*k = 225 and 7*k = 525 share the same set of digits, namely {2,5}.
k = 423 is a term because 3*k = 1269 and 7*k = 2961 share the same set of digits, namely {1,2,6,9}.

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Cf. A008585, A008589, A093140.

Select[Range[0, 11000], Union[IntegerDigits[3*#]] == Union[IntegerDigits[7*#]] &] (* Amiram Eldar, May 18 2023 *)

isok(k) = Set(digits(3*k)) == Set(digits(7*k));

def ok(n): return set(str(3*n)) == set(str(7*n))
print([k for k in range(11000) if ok(k)]) # Michael S. Branicky, May 04 2023

cp's OEIS Frontend

A093141 Expansion of (1-6x)/(1-10x).

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A362792 Numbers k such that 3k and 7k share the same set of digits.

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cp's OEIS Frontend

A093141 Expansion of (1-6*x)/(1-10*x).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions

A362792 Numbers k such that 3*k and 7*k share the same set of digits.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Python

A093141 Expansion of (1-6x)/(1-10x).

A362792 Numbers k such that 3k and 7k share the same set of digits.