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.

A030659 Smallest possible maximum denominator in an expression for 1 as a sum of n distinct unit (Egyptian) fractions.

Original entry on oeis.org

6, 12, 15, 15, 18, 20, 24, 24, 28, 30, 33, 33, 35, 36, 40, 42, 48, 52, 52, 54, 55, 55, 56, 60, 63, 72, 75, 75, 76, 76, 77, 78, 80, 85, 85, 88, 90, 95, 96, 96, 100, 102, 104, 104, 108, 110, 114, 115, 115, 119, 119, 120, 126, 130, 132, 135, 138, 143, 144, 144
Offset: 3

Views

Author

Dan Hoey

Keywords

References

  • R. K. Guy (1981): Unsolved Problems In Number Theory, D11, also p. 161.

Links

Crossrefs

Cf. A213062. - Alois P. Heinz, Sep 21 2012

Extensions

More terms from Jon E. Schoenfield, Mar 24 2014

A216975 Triangle read by rows in which row n gives the lexicographically earliest minimal sum denominators among all possible n-term Egyptian fractions with unit sum.

Original entry on oeis.org

1, 0, 0, 2, 3, 6, 2, 4, 6, 12, 3, 4, 5, 6, 20, 3, 4, 6, 10, 12, 15, 3, 4, 9, 10, 12, 15, 18, 4, 5, 6, 9, 10, 15, 18, 20, 4, 6, 8, 9, 10, 12, 15, 18, 24, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 6, 7, 8, 9, 10, 12, 14, 15, 18, 24, 28, 6, 7, 9, 10, 11, 12, 14, 15, 18, 22, 28, 33, 7, 8, 9, 10, 11, 12, 14, 15, 18, 22, 24, 28, 33
Offset: 1

Views

Author

Robert Price, Sep 21 2012

Keywords

Comments

This sequence is the lexicographically earliest Egyptian fraction (denominators only) describing the minimal sum given in A213062.
Row 2 = [0,0] corresponds to the fact that 1 cannot be written as Egyptian fraction with 2 (distinct) terms.

Examples

			Row 5 = [3,4,5,6,20]: lexicographically earliest minimal sum (38) denominators among 72 possible 5-term Egyptian fractions with unit sum.
1 = 1/3 + 1/4 + 1/5 + 1/6 + 1/20.
Triangle begins:
1;
0, 0;
2, 3, 6;
2, 4, 6, 12;
3, 4, 5,  6, 20;
3, 4, 6, 10, 12, 15;

References

  • Mohammad K. Azarian, Sylvester's Sequence and the Infinite Egyptian Fraction Decomposition of 1, Problem 958, College Mathematics Journal, Vol. 42, No. 4, September 2011, p. 330. Solution published in Vol. 43, No. 4, September 2012, pp. 340-342

Links

Crossrefs

Cf. A030659, A073546, A213062, A216993.

A216993 Triangle read by rows in which row n gives the lexicographically earliest denominators with the least possible maximum value among all n-term Egyptian fractions with unit sum.

Original entry on oeis.org

1, 0, 0, 2, 3, 6, 2, 4, 6, 12, 2, 4, 10, 12, 15, 3, 4, 6, 10, 12, 15, 3, 4, 9, 10, 12, 15, 18, 3, 5, 9, 10, 12, 15, 18, 20, 4, 5, 8, 9, 10, 15, 18, 20, 24, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 5, 6, 8, 9, 10, 15, 18, 20, 21, 24, 28, 4, 8, 9, 10, 12, 15, 18, 20, 21, 24, 28, 30, 4, 8, 9, 11, 12, 18, 20, 21, 22, 24, 28, 30, 33
Offset: 1

Views

Author

Robert Price, Sep 21 2012

Keywords

Comments

This sequence is the lexicographically earliest Egyptian fraction (denominators only) describing the minimum largest denominator given in A030659.
Row 2 = [0,0] corresponds to the fact that 1 cannot be written as an Egyptian fraction with 2 (distinct) terms.

Examples

			Row 5 = [2,4,10,12,15]: lexicographically earliest denominators with the least possible maximum value (15) among 72 possible 5-term Egyptian fractions equal to 1. 1 = 1/2 + 1/4 + 1/10 + 1/12 + 1/15.
Triangle begins:
  1;
  0, 0;
  2, 3,  6;
  2, 4,  6, 12;
  2, 4, 10, 12, 15;
  3, 4,  6, 10, 12, 15;

Links

Crossrefs

Cf. A030659, A073546, A213062, A216975, A378723.
Showing 1-3 of 3 results.

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