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 1-3 of 3 results.

A047700 Numbers that are the sum of 5 positive squares.

Original entry on oeis.org

5, 8, 11, 13, 14, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79
Offset: 1

Views

Author

Arlin Anderson (starship1(AT)gmail.com)

Keywords

Comments

Complement of A047701.

Examples

			From _David A. Corneth_, Aug 04 2020: (Start)
2009 is in the sequence as 2009 = 18^2 + 18^2 + 18^2 + 19^2 + 26^2.
2335 is in the sequence as 2335 = 19^2 + 19^2 + 20^2 + 22^2 + 27^2.
3908 is in the sequence as 3908 = 24^2 + 24^2 + 26^2 + 28^2 + 36^2. (End)

Links

Crossrefs

Cf. A000414, A003328, A047701, A294675, A344795, A344805.

Formula

a(n) = n + 12 for n >= 22. - David A. Corneth, Aug 04 2020

A344806 Numbers that are the sum of six squares in two or more ways.

Original entry on oeis.org

21, 24, 29, 30, 33, 36, 38, 39, 41, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98
Offset: 1

Views

Author

David Consiglio, Jr., Jun 20 2021

Keywords

Examples

			24 = 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 4^2
   = 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2
so 24 is a term.

Links

Crossrefs

Cf. A344795, A344805, A344807, A345479, A345511.

Programs

  • Python
    from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**2 for x in range(1, 1000)]
for pos in cwr(power_terms, 6):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v >= 2])
    for x in range(len(rets)):
        print(rets[x])

A345478 Numbers that are the sum of seven squares in one or more ways.

Original entry on oeis.org

7, 10, 13, 15, 16, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78
Offset: 1

Views

Author

David Consiglio, Jr., Jun 19 2021

Keywords

Examples

			10 is a term because 10 = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 2^2.

Links

Crossrefs

Cf. A003330, A344805, A345479, A345488, A345508.

Programs

  • Mathematica
    ssQ[n_]:=Count[IntegerPartitions[n,{7}],?(AllTrue[Sqrt[#],IntegerQ]&)]>0; Select[ Range[ 80],ssQ] (* _Harvey P. Dale, Jun 22 2022 *)
  • Python
    from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**2 for x in range(1, 1000)]
for pos in cwr(power_terms, 7):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v >= 1])
    for x in range(len(rets)):
        print(rets[x])

Formula

From Chai Wah Wu, Jun 12 2025: (Start)
All integers >= 21 are terms. See A345508 for a similar proof.
a(n) = 2*a(n-1) - a(n-2) for n > 9.
G.f.: x*(-x^8 + x^7 - x^6 + x^5 - x^4 - x^3 - 4*x + 7)/(x - 1)^2. (End)
Showing 1-3 of 3 results.

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

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