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.

User: Benjamin Hutz

Benjamin Hutz's wiki page.

Benjamin Hutz has authored 6 sequences.

A325605 Lower left-hand y-coordinate for 3 X 3 invisible forest with 0 < x < y.

Original entry on oeis.org

1308, 2000, 2330, 2714, 3128, 2540, 2924, 3080, 3484, 3794, 3730, 4654, 4730, 4234, 4640, 4718, 5300, 5564, 5654, 4928, 5704, 5654, 5718, 4598, 5654, 4640, 5642, 6200, 4640, 5150, 4598, 6094, 5984, 5984, 6408, 6460, 4674, 4794, 6104, 5620
Offset: 1

Views

Author

Benjamin Hutz, May 31 2019

Keywords

Comments

These are 3 X 3 rectangles of lattice points not visible along straight lines of sight from the origin. The sequence is ordered by Euclidean distance from (0,0).

Examples

			1308 is a term because (1274, 1308) is the lower left-hand coordinate of a 3 X 3 invisible forest, i.e., gcd(1274+i, 1308+j) > 1 for 0 <= i <= 2 and 0 <= j <= 2.
Other such coordinates are (1884, 2000), (1924, 2330), (1448, 2714), (594, 3128), (2254, 2540), (2364, 2924), (2210, 3080), (1598, 3484), (1000, 3794).

Links

Crossrefs

Cf. A157426, A157427, A157428, A157429.
Cf. A325602, A325603, A325604, A325606, A325607.

A325606 Lower left-hand x-coordinate for 4 X 4 invisible forest with 0 < x < y.

Original entry on oeis.org

7247643, 6349914, 13449225, 3268473, 16799913, 12209988, 7676094, 25869732, 27330093, 19113828, 3689958, 8579373, 35193585, 10557390, 31662993, 40976505, 20262723, 47516988, 12932424, 10792494, 13027728, 24801060, 44040840, 37959282, 42196362, 16439577, 43732038
Offset: 1

Views

Author

Benjamin Hutz, May 31 2019

Keywords

Comments

These are 4 X 4 rectangles of lattice points not visible along straight lines of sight from the origin. The sequence is ordered by Euclidean distance from (0,0).

Examples

			(7247643, 10199370), (6349914, 13125369), (13449225, 13458288), (3268473, 21374352), (16799913, 22339875)

Links

Crossrefs

Cf. A157426, A157427, A157428, A157429.
Cf. A325602, A325603, A325604, A325605, A325607.

Extensions

a(6)-a(27) from Giovanni Resta, Jun 05 2019

A325607 Lower left-hand y-coordinate for 4 X 4 invisible forest with 0 < x < y.

Original entry on oeis.org

10199370, 13125369, 13458288, 21374352, 22339875, 29634813, 39738060, 32719728, 42182412, 47211294, 51258282, 53418859, 43209969, 55756413, 48330114, 49362234, 62965329, 52850433, 72584082, 73167345, 73891893, 71088744, 61716444, 66526029, 69342999, 80514873, 71127132
Offset: 1

Views

Author

Benjamin Hutz, May 31 2019

Keywords

Comments

These are 4 X 4 rectangles of lattice points not visible along straight lines of sight from the origin. The sequence is ordered by Euclidean distance from (0,0).

Examples

			(7247643, 10199370), (6349914, 13125369), (13449225, 13458288), (3268473, 21374352), (16799913, 22339875)

Links

Crossrefs

Cf. A157426, A157427, A157428, A157429.
Cf. A325602, A325603, A325604, A325605, A325606.

Extensions

a(6)-a(27) from Giovanni Resta, Jun 05 2019

A325604 Lower left-hand x-coordinate for 3 X 3 invisible forest with 0 < x < y.

Original entry on oeis.org

1274, 1884, 1924, 1448, 594, 2254, 2364, 2210, 1598, 1000, 2624, 740, 664, 2408, 1924, 1924, 494, 1000, 230, 2914, 650, 1000, 644, 3794, 1924, 3794, 2430, 104, 4146, 3534, 4234, 1748, 2254, 2408, 1274, 1064, 4640, 4520, 2484, 3794
Offset: 1

Views

Author

Benjamin Hutz, May 10 2019

Keywords

Comments

These are 3 X 3 rectangles of lattice points not visible along straight lines of sight from the origin. The sequence is ordered by Euclidean distance from (0,0).

Examples

			(1274,1308), (1884,2000), (1924,2330), (1448,2714), (594,3128), (2254,2540), (2364,2924), (2210,3080), (1598,3484), (1000,3794)

Links

Crossrefs

Cf. A157426, A157427, A157428, A157429.
Cf. A325602, A325603, A325605, A325606, A325607.

A325602 Lower left-hand x-coordinate for 2 X 2 invisible forest with 0 < x < y.

Original entry on oeis.org

14, 14, 20, 44, 39, 21, 45, 34, 50, 21, 44, 39, 54, 75, 45, 65, 34, 77, 74, 69, 90, 56, 50, 84, 76, 33, 84, 14, 20, 69, 55, 111, 75, 33, 14, 105, 35, 119, 95, 20, 56, 35, 74, 90, 110, 104, 76, 62, 20, 35
Offset: 1

Views

Author

Benjamin Hutz, May 10 2019

Keywords

Comments

These are 2 X 2 rectangles of lattice points not visible along straight lines of sight from the origin. The sequence is ordered by Euclidean distance from (0,0).

Examples

			(14,20), (14,35), (20,35), (44,54), (39,65), (21,77), (45,69), (34,84), ...

Links

Crossrefs

Cf. A157426, A157427, A157428, A157429.
Cf. A325603, A325604, A325605, A325606, A325607.

Programs

  • Python
    def is_nxn(x,y,n):
    if all([gcd(x+a,y+b) != 1 for a in range(n) for b in range(n)]):
        return True
    return False
def insert_item(pts, item, index):
    N = len(pts)
    if N == 0:
      return [item]
    elif N == 1:
        if item[index] < pts[0][index]:
            pts.insert(0,item)
        else:
            pts.append(item)
        return pts
    else: #binary insertion
        left = 1
        right = N
        mid = ((left + right)/2).floor()
        if item[index] < pts[mid][index]:
        # item goes into first half
            return insert_item(pts[:mid], item, index) + pts[mid:N]
        else:
        # item goes into second half
            return pts[:mid] + insert_item(pts[mid:N], item, index)
B=1200
L=[]
for x in range(1,B):
    for y in range(x+1,B):
        if is_nxn(x,y,n=2):
            G=[x,y,x^2+y^2]
            L=insert_item(L, G, 2)

A325603 Lower left-hand y-coordinate for 2 X 2 invisible forest with 0 < x < y.

Original entry on oeis.org

20, 35, 35, 54, 65, 77, 69, 84, 84, 98, 99, 104, 99, 95, 114, 104, 119, 98, 110, 114, 104, 132, 135, 119, 132, 153, 135, 174, 174, 161, 175, 147, 170, 186, 189, 159, 189, 153, 170, 195, 189, 195, 185, 195, 185, 195, 209, 216, 224, 224
Offset: 1

Views

Author

Benjamin Hutz, May 10 2019

Keywords

Comments

These are 2 X 2 rectangles of lattice points not visible along straight lines of sight from the origin. The sequence is ordered by Euclidean distance from (0,0).

Examples

			(14,20), (14,35), (20,35), (44,54), (39,65), (21,77), (45,69), (34,84).

Links

Crossrefs

Cf. A157426, A157427, A157428, A157429, A325602, A325604, A325605, A325606, A325607.

Programs

  • SageMath
    def is_nxn(x,y,n):
    if all([gcd(x+a,y+b) != 1 for a in range(n) for b in range(n)]):
        return True
    return False
def insert_item(pts, item, index):
    N = len(pts)
    if N == 0:
      return [item]
    elif N == 1:
        if item[index] < pts[0][index]:
            pts.insert(0,item)
        else:
            pts.append(item)
        return pts
    else: #binary insertion
        left = 1
        right = N
        mid = ((left + right)/2).floor()
        if item[index] < pts[mid][index]:
        # item goes into first half
            return insert_item(pts[:mid], item, index) + pts[mid:N]
        else:
        # item goes into second half
            return pts[:mid] + insert_item(pts[mid:N], item, index)
B=1200
L=[]
for x in range(1,B):
    for y in range(x+1,B):
        if is_nxn(x,y,n=2):
            G=[x,y,x^2+y^2]
            L=insert_item(L, G, 2)

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

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