The On-Line Encyclopedia of Integer Sequences (OEIS)

Revisions by Mike Sheppard

(See also Mike Sheppard's wiki page)

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A033810

Number of people needed so that probability of at least two sharing a birthday out of n possible days is at least 50%.
(history; published version)

#89 by Mike Sheppard at Fri Jan 17 14:18:24 EST 2025

STATUS

editing

proposed

#88 by Mike Sheppard at Fri Jan 17 14:18:19 EST 2025

CROSSREFS

Cf. A380129 (Strong Birthday Problem)

STATUS

approved

editing

A380175

allocated for Mike Sheppard
(history; published version)

#23 by Mike Sheppard at Thu Jan 16 17:55:22 EST 2025

STATUS

editing

proposed

#21 by Mike Sheppard at Wed Jan 15 17:30:35 EST 2025

DATA

0, 1, 4, 5, 9, 10, 13, 14, 16, 17, 20, 21, 25, 26, 29, 30, 34, 35, 36, 37, 40, 41, 45, 46, 49, 50, 53, 54, 58, 59, 62, 63, 64, 65, 68, 69, 73, 74, 77, 78, 80, 81, 82, 85, 86, 90, 91, 94, 95, 97, 98, 100, 101, 104, 105, 109, 110, 113, 114, 116, 117, 120, 121, 122, 125, 126, 130

OFFSET

1,23

STATUS

proposed

editing

Discussion

Wed Jan 15

17:31

Mike Sheppard: Updated to include 0 per Michael S. Branicky suggestion and that the Montgomery reference states "It is convenient to set a(0) = 1"  (their a(n) is an indicator function)

19:11

Michael S. Branicky: Thanks. It is also now consistent with your A380177 starting with 38 since 0 is a term in A003995.

#16 by Mike Sheppard at Wed Jan 15 08:09:59 EST 2025

STATUS

editing

proposed

Discussion

Wed Jan 15

08:55

Mike Sheppard: Correct, depends on the final remainder less than 9.   "Thus the question of whether the summands are distinct depends entirely on the first remainder less than 9. If this remainder is one of numbers 0,1,4, or 5, then the summands are distinct, but if it is one of the numbers 2,3,6,7 or 8, then they are not"

#15 by Mike Sheppard at Wed Jan 15 08:08:33 EST 2025

MATHEMATICA

getLargestSquares[n_Integer] := Module[{remaining = n, squares = {}}, While[remaining > 0, AppendTo[squares, Floor[Sqrt[remaining]]]; remaining -= Last[squares]^2; ]; squares];

a = Select[Range[200], Length[#] == Length[DeleteDuplicates[#]] &@getLargestSquares[#] &]

DuplicateFreeQ[#] &@

Differences[NestWhileList[# - Floor[Sqrt[#]]^2 &, #, # > 0 &]] &]

STATUS

proposed

editing

Discussion

Wed Jan 15

08:09

Mike Sheppard: Simplified program.

#5 by Mike Sheppard at Tue Jan 14 23:36:54 EST 2025

STATUS

editing

proposed

#4 by Mike Sheppard at Tue Jan 14 23:36:26 EST 2025

MATHEMATICA

getLargestSquares[n_Integer] := Module[{remaining = n, squares = {}}, While[remaining > 0, AppendTo[squares, Floor[Sqrt[remaining]]]; remaining -= Last[squares]^2; ]; squares];

a = Select[Range[200], Length[#] == Length[DeleteDuplicates[#]] &@getLargestSquares[#] &]

STATUS

proposed

editing

Discussion

Tue Jan 14

23:36

Mike Sheppard: Added Mathematica program

A380177

allocated for Mike Sheppard
(history; published version)

#3 by Mike Sheppard at Tue Jan 14 23:32:17 EST 2025

STATUS

editing

proposed

#2 by Mike Sheppard at Tue Jan 14 23:31:36 EST 2025

NAME

allocated for Mike Sheppard

Can be written as sum of distinct squares but not if taken greedily

DATA

38, 39, 42, 51, 52, 55, 56, 57, 61, 66, 70, 71, 75, 79, 83, 84, 87, 88, 89, 93, 99, 102, 103, 106, 107, 111, 115, 118, 119, 123, 124, 127, 129, 132, 133, 136, 139, 140, 143, 146, 147, 150, 151, 152, 155, 156, 159, 162, 163, 166, 167, 168, 171, 172, 175, 176, 177, 180, 181, 184, 187, 188, 191, 192, 193, 198, 199

OFFSET

1,1

COMMENTS

38 is in the list as 38 = 5^2 + 3^2 + 2^2, all distinct; but if taken greedily 38 = 6^2 + 1^2 + 1^2, not distinct. Greedily in the sense that 6^2 < 38 < 7^2 etc.

Numbers in A003995 but not in A380175; 38 is the first

REFERENCES

Montgomery, Hugh, and Ulrike Vorhauer. "Greedy sums of distinct squares." Mathematics of computation 73.245 (2004): 493-513.

KEYWORD

allocated

nonn

AUTHOR

Mike Sheppard, Jan 14 2025

STATUS

approved

editing