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.

A028820 Squares with digits in nondecreasing order.

Original entry on oeis.org

0, 1, 4, 9, 16, 25, 36, 49, 144, 169, 225, 256, 289, 1156, 1225, 1369, 1444, 4489, 6889, 11236, 11449, 13456, 13689, 27889, 33489, 111556, 112225, 113569, 134689, 146689, 344569, 444889, 2666689, 2778889, 11115556, 11122225, 11135569
Offset: 1

Views

Author

Patrick De Geest

Keywords

Comments

Number of terms less than 10^k, beginning with k=0: 1, 4, 8, 13, 19, 25, 32, 34, 42, 43, 50, 53, 61, 62, 71, 72, 82, 83, 94, 95, …, .
Like all squares the ending digits can be 0, 1, 4, 5, 6 or 9. Here is the tally of the list of terms < 10^19: {0, 1}, {1, 1}, {4, 4}, {5, 10}, {6, 13}, {9, 66}. Robert G. Wilson v, Jan 01 2014

Links

Crossrefs

Cf. A028819, A028821, A028822, A237424.
Intersection of A000290 and A009994.

Programs

  • Mathematica
    Select[Range[0,4000]^2,Min[Differences[IntegerDigits[#]]]>-1&] (* Harvey P. Dale, Dec 31 2013 *)
Select[Range[0,10^4]^2,LessEqual@@IntegerDigits[#]&] (* Ray Chandler, Jan 06 2014 *)
  • PARI
    mono(n)=n=eval(Vec(Str(n)));for(i=2,#n,if(n[i]Charles R Greathouse IV, Aug 22 2011
  • Python
    from itertools import combinations_with_replacement
from gmpy2 import is_square
A028820_list = [0] + [n for n in (int(''.join(i)) for l in range(1,11) for i in combinations_with_replacement('123456789',l)) if is_square(n)] # Chai Wah Wu, Dec 07 2015

Formula

a(n) = A028819(n)^2. - Ray Chandler, Jan 06 2014

Extensions

Definition edited by Zak Seidov, Dec 31 2013

A028821 Numbers k such that k^2 has digits in nonincreasing order.

Original entry on oeis.org

0, 1, 2, 3, 8, 9, 10, 20, 21, 29, 30, 31, 80, 88, 90, 100, 200, 210, 290, 300, 310, 800, 880, 900, 1000, 2000, 2100, 2900, 2979, 3000, 3100, 3139, 8000, 8800, 9000, 10000, 20000, 21000, 29000, 29790, 30000, 31000, 31390, 31621, 80000, 88000
Offset: 1

Views

Author

Patrick De Geest

Keywords

Links

Crossrefs

Cf. A028822.

Programs

  • Mathematica
    Select[Range[0,10^5],GreaterEqual@@IntegerDigits[#^2]&] (* Ray Chandler, Jan 05 2014 *)

Extensions

Better name from Ray Chandler, Jan 05 2014

A062826 Square nialpdromes not ending in 0.

Original entry on oeis.org

1, 4, 9, 64, 81, 441, 841, 961, 7744, 8874441, 9853321, 999887641
Offset: 1

Views

Author

David W. Wilson, Jul 20 2001

Keywords

Comments

Probably finite.
There are no more terms up to 10^11. - Charles R Greathouse IV, Jan 02 2014
No more terms up to 10^42. - Chai Wah Wu, Dec 07 2015

Crossrefs

Nialpdromes are A009996. Square nialpdromes are A028822.

Programs

  • Maple
    F:= proc(x) local L; L:= convert(x,base,10); max(L[1..-2] - L[2..-1]) <= 0 end proc:
select(F, [seq(seq((10*x+y)^2,y=1..9),x=0..10^6)]); # Robert Israel, Dec 08 2015

A355063 Perfect powers whose digits are in nonincreasing order and do not include 0.

Original entry on oeis.org

1, 4, 8, 9, 32, 64, 81, 441, 841, 961, 7744, 7776, 8874441, 9853321, 999887641
Offset: 1

Views

Author

Jon E. Schoenfield, Jun 16 2022

Keywords

Comments

a(16) > 10^45 if it exists. - Michael S. Branicky, Jun 19 2022

Crossrefs

Cf. A001597, A009996, A028822, A062826.

Programs

  • Mathematica
    perfectPowerQ[n_] := n==1||GCD @@ FactorInteger[n][[All, 2]] > 1; (* A001597 *) Select[Range[10^5], perfectPowerQ[#] && Max[Differences[d=IntegerDigits[#]]]<1 && Count[d,0]==0&] (* Stefano Spezia, Jul 01 2025 *)
  • PARI
    isok(m) = if (ispower(m), my(d=digits(m)); vecmin(d) && (d == vecsort(d,,4))); \\ Michel Marcus, Jun 17 2022
  • Python
    from sympy import perfect_power as pp
from itertools import count, islice, combinations_with_replacement as mc
def agen():
    yield 1
    for d in count(1):
        nd = (int("".join(m)) for m in mc("987654321", d))
        yield from sorted(filter(pp, nd))
print(list(islice(agen(), 14))) # Michael S. Branicky, Jun 16 2022

A124683 Squares with strictly decreasing digits.

Original entry on oeis.org

0, 1, 4, 9, 64, 81, 841, 961
Offset: 1

Views

Author

Tanya Khovanova, Dec 24 2006

Keywords

Crossrefs

Cf. A122683 = squares with increasing digits. Subsequence of A028822 = squares with digits in descending order.

Extensions

0 inserted by Jon E. Schoenfield, Jan 15 2014
Showing 1-5 of 5 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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