Scott R. Shannon - cp's OEIS frontend

A383934 Composite numbers that contain only nonprime digits and whose prime factors contain only nonprime digits.

1111, 1199, 1681, 1691, 1919, 1991, 4141, 4411, 4469, 4499, 4609, 4961, 6109, 6161, 6611, 6649, 6809, 8899, 8989, 9089, 9481, 9691, 10109, 10901, 11009, 11041, 11099, 11419, 11881, 14641, 14801, 16109, 16441, 16489, 16999, 18409, 18491, 18601, 18689

Offset: 1

Scott R. Shannon, Aug 17 2025

			10109 is a term as 10109 = 11 * 919, and both the number and its prime factors only contain nonprime digits.

Scott R. Shannon, Table of n, a(n) for n = 1..10000

Cf. A084984, A018252, A387093, A000040.

Select[Select[Range[20000], And[CompositeQ[#], NoneTrue[IntegerDigits[#], PrimeQ]] &], NoneTrue[Flatten[IntegerDigits /@ FactorInteger[#][[All, 1]] ], PrimeQ] &] (* Michael De Vlieger, Aug 23 2025 *)

A387093 Composite numbers that contain only prime digits and whose prime factors contain only prime digits.

Original entry on oeis.org

25, 27, 32, 35, 72, 75, 222, 225, 252, 322, 333, 375, 525, 552, 555, 575, 735, 777, 2352, 2553, 2555, 2775, 3357, 3375, 3552, 3577, 5222, 5352, 5575, 7252, 7322, 23253, 23373, 23532, 23535, 23552, 25275, 25725, 25737, 27232, 27252, 27375, 32352, 32375

Offset: 1

Scott R. Shannon and Ursula Ponting, Aug 16 2025

			25725 is a term as 25725 = 3 * 5^2 * 7^3, and both the number and its prime factors only contain prime digits.

Scott R. Shannon, Table of n, a(n) for n = 1..2298 (all terms < 10^12).

Cf. A061371, A027746, A000040, A019546.

Select[Select[Range[33000], CompositeQ], And[AllTrue[Union@ IntegerDigits[#], PrimeQ], AllTrue[Union@ Flatten@ Map[IntegerDigits, FactorInteger[#][[All, 1]] ], PrimeQ]] &] (* Michael De Vlieger, Aug 16 2025 *)

A386775 Place a point on the integer coordinates, up to |k|, along all four axial directions on a Cartesian plane, and then join an infinite straight line between every pair of points: a(n) is the smallest k such that n lines intersect at a point not on the axes.

Original entry on oeis.org

2, 3, 4, 6, 8, 9, 9, 10, 14, 16, 18, 20, 24, 25, 26, 30, 34, 36

Offset: 2

Scott R. Shannon, Aug 02 2025

See A386559 for images of the graph intersections.

			a(9) = 10 as the following 9 lines all intersect at the point (4,3) while having |x| and |y| intercepts <= 10 :
.
   equation    |  y-intercept  |  x-intercept
-------------------------------------------------
   -3/2*x + 9  |       9       |       6
       -x + 7  |       7       |       7
   -3/4*x + 6  |       6       |       8
   -1/2*x + 5  |       5       |      10
    1/4*x + 2  |       2       |      -8
    1/2*x + 1  |       1       |      -2
        x - 1  |      -1       |       1
    3/2*x - 3  |      -3       |       2
      3*x - 9  |      -9       |       3
-------------------------------------------------

Cf. A386559.

A386560 Place a point on the integer coordinates, up to |n|, along all four axial directions on a Cartesian plane, and then join an infinite straight line between every pair of points: a(n) is the number of finite regions created in the resulting graph.

Original entry on oeis.org

4, 72, 424, 1396, 3536, 7292, 14272, 24332, 39356, 59920, 91348, 128084, 182664, 245804, 323116, 418552, 547820, 684680, 869388, 1060892, 1289564, 1560920

Offset: 1

Scott R. Shannon, Jul 26 2025

Scott R. Shannon, Image for n = 1. In this and other images the integer coordinates are highlighted as white dots while the outer open regions, which are not counted, are darkened.
Scott R. Shannon, Image for n = 2.
Scott R. Shannon, Image for n = 3.
Scott R. Shannon, Image for n = 4.
Scott R. Shannon, Image for n = 5

Cf. A386559 (vertices), A386561 (edges), A386562 (k-gons), A344993, A344857, A344279, A345459.

a(n) = A386561(n) - A386559(n) + 1 by Euler's formula.

A386559 Place a point on the integer coordinates, up to |n|, along all four axial directions on a Cartesian plane, and then join an infinite straight line between every pair of points: a(n) is the number of points where lines intersect in the resulting graph.

Original entry on oeis.org

5, 65, 381, 1213, 3033, 6105, 12285, 20789, 33705, 51065, 79797, 110817, 161549, 216985, 284269, 367925, 489953, 609225, 785045, 952877, 1157749, 1404473

Offset: 1

Scott R. Shannon, Jul 26 2025

It appears that for n >= 3 the intersection that is furthest from the origin is formed by the crossing of the lines y = n/(n-1)*x + n and y = (n-1)/(n-2)*x - (n-1), along with the seven other symmetrically equivalent intersections. These intersections have a distance from the origin of approximately sqrt(8)*n^3 as n -> infinity.

Scott R. Shannon, Image for n = 1.
Scott R. Shannon, Image for n = 2.
Scott R. Shannon, Image for n = 3.
Scott R. Shannon, Image for n = 4.

Cf. A386560 (regions), A386561 (edges), A386562 (k-gons), A146212, A347750, A344657, A345649.

a(n) = A386561(n) - A386560(n) + 1 by Euler's formula.

A386561 Place a point on the integer coordinates, up to |n|, along all four axial directions on a Cartesian plane, and then join an infinite straight line between every pair of points: a(n) is the number of finite edges created in the resulting graph.

Original entry on oeis.org

8, 136, 804, 2608, 6568, 13396, 26556, 45120, 73060, 110984, 171144, 238900, 344212, 462788, 607384, 786476, 1037772, 1293904, 1654432, 2013768, 2447312, 2965392

Offset: 1

Scott R. Shannon, Jul 26 2025

See A386559 and A386560 for images of the graphs.

Cf. A386559 (vertices), A386560 (regions), A386562 (k-gons), A347751, A344899, A344896, A345650.

a(n) = A386559(n) + A386560(n) - 1 by Euler's formula.

A386562 Irregular table read by rows: Place a point on the integer coordinates, up to |n|, along all four axial directions on a Cartesian plane, and then join an infinite straight line between every pair of points: T(n,k) is the number of k-sided finite polygons formed, for k>=3, in the resulting graph.

Original entry on oeis.org

4, 44, 24, 4, 184, 216, 24, 560, 780, 56, 1456, 1844, 224, 12, 3100, 3788, 376, 24, 4, 5860, 7100, 1148, 156, 8, 9860, 12436, 1848, 164, 20, 4, 16044, 19732, 3100, 460, 16, 4, 24744, 29568, 5048, 516, 32, 12, 36780, 43472, 9608, 1400, 68, 20, 52296, 61244, 12628, 1784, 116, 16

Offset: 1

Scott R. Shannon, Jul 26 2025

For graphs up to n = 22 the k-gons with the largest number of sides are 12-gons, first appearing for n = 20. The behavior of this maximum value as n -> infinity is unknown.

See A386559 and A386560 for other images of the graphs.

			The table begins:
4;
44, 24, 4;
184, 216, 24;
560, 780, 56;
1456, 1844, 224, 12;
3100, 3788, 376, 24, 4;
5860, 7100, 1148, 156, 8;
9860, 12436, 1848, 164, 20, 4;
16044, 19732, 3100, 460, 16, 4;
24744, 29568, 5048, 516, 32, 12;
36780, 43472, 9608, 1400, 68, 20;
52296, 61244, 12628, 1784, 116, 16;
72492, 85672, 20424, 3792, 268, 16;
97812, 115000, 27796, 4820, 344, 24, 8;
129416, 151184, 35716, 6240, 532, 28;
167712, 195816, 46380, 7956, 644, 44;
.
.

Scott R. Shannon, Image for n = 2. The integer coordinates are highlighted as white dots while the outer open regions, which are not counted, are darkened.

Cf. A386559 (vertices), A386560 (regions), A386561 (edges), A344938, A346446.

Sum of row n = A386560(n).

A385162 Place a point on the integer coordinates, up to |n|, along all four axial directions on a Cartesian plane, and then join a circle through every unordered triple of non-collinear points: a(n) is the number of distinct (curved) edges formed from the intersections of the circles.

Original entry on oeis.org

4, 184, 8956, 79272, 455664, 1420624, 4576632

Offset: 1

Scott R. Shannon, Jul 10 2025

Scott R. Shannon, Image for n = 2. The 4 x 2 = 8 starting points are shown as white dots.

Cf. A385159 (total circles), A385160 (vertices), A385161 (regions), A384703, A374827, A373108, A359571.

a(n) = A385160(n) + A385161(n) - 1 by Euler's formula.

A385161 Place a point on the integer coordinates, up to |n|, along all four axial directions on a Cartesian plane, and then join a circle through every unordered triple of non-collinear points: a(n) is the number of distinct (finite) regions created.

Original entry on oeis.org

1, 117, 4713, 41173, 233365, 725081, 2323869

Offset: 1

Scott R. Shannon, Jul 10 2025

Scott R. Shannon, Image for n = 2. The 4 x 2 = 8 starting points are shown as white dots.
Scott R. Shannon, Image for n = 3. The 4 x 3 = 12 starting points are shown as white dots.

Cf. A385159 (total circles), A385160 (vertices), A385162 (edges), A384702, A374826, A372977, A359570.

a(n) = A385162(n) - A385160(n) + 1 by Euler's formula.

A385160 Place a point on the integer coordinates, up to |n|, along all four axial directions on a Cartesian plane, and then join a circle through every unordered triple of non-collinear points: a(n) is the number of distinct points where circles intersect.

Original entry on oeis.org

4, 68, 4244, 38100, 222300, 695544, 2252764

Offset: 1

Scott R. Shannon, Jul 10 2025

Scott R. Shannon, Image for n = 2. The 4 x 2 = 8 starting points are shown as white dots.
Scott R. Shannon, Image for n = 3. The 4 x 3 = 12 starting points are shown as white dots.

Cf. A385159 (total circles), A385161 (regions), A385162 (edges), A384703, A383461, A374825, A359569.

a(n) = A385162(n) - A385161(n) + 1 by Euler's formula.

cp's OEIS Frontend

User: Scott R. Shannon

A383934 Composite numbers that contain only nonprime digits and whose prime factors contain only nonprime digits.

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Mathematica

A387093 Composite numbers that contain only prime digits and whose prime factors contain only prime digits.

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Programs

Mathematica

A386775 Place a point on the integer coordinates, up to |k|, along all four axial directions on a Cartesian plane, and then join an infinite straight line between every pair of points: a(n) is the smallest k such that n lines intersect at a point not on the axes.

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Examples

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A386560 Place a point on the integer coordinates, up to |n|, along all four axial directions on a Cartesian plane, and then join an infinite straight line between every pair of points: a(n) is the number of finite regions created in the resulting graph.

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Author

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A386559 Place a point on the integer coordinates, up to |n|, along all four axial directions on a Cartesian plane, and then join an infinite straight line between every pair of points: a(n) is the number of points where lines intersect in the resulting graph.

Views

Author

Keywords

Comments

Links

Crossrefs

Formula

A386561 Place a point on the integer coordinates, up to |n|, along all four axial directions on a Cartesian plane, and then join an infinite straight line between every pair of points: a(n) is the number of finite edges created in the resulting graph.

Views

Author

Keywords

Comments

Crossrefs

Formula

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A385162 Place a point on the integer coordinates, up to |n|, along all four axial directions on a Cartesian plane, and then join a circle through every unordered triple of non-collinear points: a(n) is the number of distinct (curved) edges formed from the intersections of the circles.

Views

Author

Keywords

Links

Crossrefs

Formula

A385161 Place a point on the integer coordinates, up to |n|, along all four axial directions on a Cartesian plane, and then join a circle through every unordered triple of non-collinear points: a(n) is the number of distinct (finite) regions created.

Views

Author

Keywords

Links

Crossrefs

Formula

A385160 Place a point on the integer coordinates, up to |n|, along all four axial directions on a Cartesian plane, and then join a circle through every unordered triple of non-collinear points: a(n) is the number of distinct points where circles intersect.

Views

Author

Keywords

Links

Crossrefs

Formula