cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

A052069 a(n)^2 is the smallest square whose digits occur with the same frequency n.

Original entry on oeis.org

0, 88, 10011, 31646191, 16431563, 667567716, 10715008859, 652246443112, 15647628653832, 781035313645040
Offset: 1

Views

Author

Patrick De Geest, Jan 15 2000

Keywords

Examples

			31646191^2 = 1001481404808481 and its digits 0, 1, 4 and 8 each occur four times.
		

Crossrefs

Programs

  • Mathematica
    Table[i = 0;
    While[x = i^2; Union@DeleteCases[DigitCount[x], 0] != {n}, i++];
    i, {n, 10}] (* Robert Price, Oct 12 2019 *)

Extensions

2 more terms from Jon E. Schoenfield, Aug 18 2007
a(10) from Giovanni Resta, Aug 19 2018

A052072 Smallest cubes whose digits occur with the same frequency n.

Original entry on oeis.org

0, 1331, 700227072, 22676697737363992239, 1728999927211172788179288, 256263633328535368685258882625, 19194114355415391344355399945943513, 2342441231418833141828248411332348812823
Offset: 1

Views

Author

Patrick De Geest, Jan 15 2000

Keywords

Examples

			22676697737363992239 (= 2830479^3) and its digits 2, 3, 6, 7 and 9 each occur four times.
		

Crossrefs

Programs

  • Mathematica
    Table[i = 0;
    While[x = i^3; Union@DeleteCases[DigitCount[x], 0] != {n}, i++];
    x, {n, 7}] (* Robert Price, Oct 12 2019 *)
    Select[Range[400]^3,Length[Union[DeleteCases[DigitCount[#],0]]]==1&] (* Harvey P. Dale, Apr 30 2022 *)
  • Python
    def A052072(n):
        a, b, c = 0, 0, 0
        for i in range(10**9):
            s = str(c)
            for d in set(s):
                if s.count(d) != n:
                    break
            else:
                return c
            c += a + b + 1
            b += 2*a + 3
            a += 3
        return 'search limit reached.'  # Chai Wah Wu, Aug 11 2015

Extensions

Offset corrected by Michel Marcus, Aug 12 2015
a(7) from Giovanni Resta, Aug 19 2018
a(8) from Mihael Tunik, May 26 2025

A052060 Numbers n such that the digits of 2^n occur with the same frequency.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 20, 29
Offset: 1

Views

Author

Patrick De Geest, Jan 15 2000

Keywords

Comments

Previous name was "Smallest power of 2 whose digits occur with same frequency n".
Next term > 3597.
Not multiplicative since a(18) is supposedly > 3597, but a(2) = 2 and a(9) = 9. - David W. Wilson, Jun 12 2005
From Robert Israel, Aug 14 2015: (Start)
Next term (if any) > 10^4.
It is highly likely that the sequence is finite. For each m, there are at most 4 powers of 2 with m digits. If m is large, of the 9*10^m numbers with m digits, there are at most about c * 10^m/m^(9/2) with equal digit frequencies where c is a constant (this comes from the case where there all 10 digits are represented with frequencies m/10). Thus heuristically the expected number of m-digit powers of 2 with equal digit frequencies decreases like m^(-9/2), and this has a finite sum. (End)

Examples

			E.g., 2^29 = 536870912 where each digit occurs once in this case.
		

Crossrefs

Programs

  • Maple
    filter:= proc(n) local x,i,P;
    P:= add(x^i,i=convert(2^n,base,10));
    nops({coeffs(P,x)})=1
    end proc:
    select(filter, [$1..10^4]); # Robert Israel, Aug 14 2015

Extensions

Name and offset corrected by Michel Marcus, Aug 12 2015

A052094 Smallest fourth powers whose decimal expansion digits occur with same frequency n.

Original entry on oeis.org

0, 1836036801, 289123718973983667216, 1051315345334684056886604801, 33065106952901022329359695121613056, 112265125207703310302573655130362165067776, 1010922420949465152104650155209626996061445542961
Offset: 1

Views

Author

Patrick De Geest, Jan 15 2000

Keywords

Comments

Terms calculated by Jeff Heleen.

Examples

			207^4 = 1836036801 and digits 0,1,3,6 and 8 each occur twice.
		

Crossrefs

Subsequence of A000583.

Programs

Extensions

Offset corrected by Michel Marcus, Aug 12 2015
a(6) corrected and a(7) from Michael S. Branicky, Dec 17 2020

A052099 Smallest nonzero square with n distinct digits each occurring exactly n times.

Original entry on oeis.org

1, 7744, 100220121, 1001481404808481, 1000049919014961464966416, 100000011325773371773233151572525225, 1000000011111863263563888125532588566228326235536
Offset: 1

Views

Author

Patrick De Geest, Jan 15 2000

Keywords

Comments

Obviously can contain at most 10 terms.

Crossrefs

Cf. A052070. - R. J. Mathar, Oct 14 2008

Extensions

a(5) from Jon E. Schoenfield, Jul 17 2010
Offset corrected and a(6)-a(7) from Donovan Johnson, Apr 16 2011
Showing 1-5 of 5 results.