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.

A235142 Numbers k such that A235141(k) = -1.

Original entry on oeis.org

4, 10, 22, 32, 64, 84, 108, 132, 186, 214, 284, 360, 446, 490, 590, 642, 694, 746, 930, 990, 1192, 1266, 1342, 1568, 1738, 2086, 2180, 2276, 2470, 2572, 2668, 2780, 3326, 3556, 3680, 3922, 4298, 4430, 4560, 4832, 4968
Offset: 1

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Author

Rajan Murthy, Jan 03 2014

Keywords

Comments

The positions reflect square radii which are uniquely twice a square integer, that is, the completion of only one square on the y = x line.

Examples

			For n = 2, a(2) = 10.  The 10th term of A235141 is -1 corresponding to the square radius of an origin centered circle increasing from the open interval(5,8) to exactly 8.

Crossrefs

A000548(n) = (A001481(1 + a(n)/2 ) )/2.
Cf. A235141, A234300.

Formula

a(n) = A235386(n+1) - 1.

A235143 Positions of -2 in A235141, the first differences of A234300.

Original entry on oeis.org

8, 14, 16, 20, 24, 26, 28, 30, 34, 38, 40, 42, 44, 50, 52, 54, 56, 62, 66, 68, 70, 74, 78, 80, 82, 86, 88, 90, 92, 94, 96, 98, 100, 104, 112, 114, 120, 122, 124, 126, 128, 130, 134, 136, 140, 142, 144, 146, 150, 152, 156, 160, 164, 166, 168, 172, 174, 176, 178, 180, 182, 184, 188, 190, 196, 200, 204
Offset: 1

Views

Author

Rajan Murthy, Jan 03 2014

Keywords

Comments

The positions reflect radii which are a unique sum of two and only two distinct nonzero square integers.
The positions are a bit less frequent in occurrence than the positions where the first differences equal 2 because when the radius changes from exactly an integer value k to the open interval (k,k+1), the number of edge squares increase by 2, while in the reverse case, an increase from the open interval (k,k+1) to exactly k+1, the number of edge squares stays the same rather than decreasing by 2 as occurs in cases when the radii are a sum of two and only two distinct nonzero square integers. This is in contrast to positions where the first difference of A234300 equals 1 which are exactly balanced by positions which equal -1.

Examples

			a(1) = 8 which corresponds to the transition of the square radius from the interval (4,5) to 5 = 1^2 + 2^2.
a(2) = 14 which corresponds to the transition from (9,10) to 10 = 1^2 + 3^2.

Links

Crossrefs

Cf. A235141, A234300, A235142, A235386.

A235387 Positions of 2's in A235141, the first differences of A234300.

Original entry on oeis.org

3, 7, 9, 13, 15, 17, 19, 21, 25, 29, 31, 35, 37, 39, 41, 43, 45, 47, 51, 53, 55, 57, 59, 63, 67, 69, 71, 73, 75, 79, 81, 83, 89, 91, 93, 95, 97, 99, 101, 103, 105, 113, 115, 117, 121, 123, 125, 127, 129, 131, 135, 141, 143, 145, 147, 151, 153, 155, 157, 161, 165, 167, 169, 175, 177, 179, 181
Offset: 1

Views

Author

Rajan Murthy, Jan 08 2014

Keywords

Comments

The positions reflect radii which are a unique sum of two distinct square integers where order doesn't matter.
The positions are more frequent in occurrence than the positions where the first differences equal -2 because when the radius changes from exactly an integer value k to the open interval (k,k+1), the number of edge squares increases by 2, while in the reverse case, an increase from the open interval (k,k+1) to exactly k+1, the number of edge squares stays the same. This is in contrast to positions where the first difference equals 1 which are exactly balanced by positions which equal -1 .

Examples

			a(2) = 7 corresponding to the shift from squared radius of 4 to (4,5).  This also marks a shift of the radius from 2 to (2,3).  The preceding shift, A235141(6), from radius in the interval (1,2) to 2 and squared radius in the interval (2,4) to 4 does not change the number of edge squares.
a(3) = 9 corresponding to the shift from squared radius of 5 to (5,8).  The radius however remains in the interval (2,3).  The preceding shift, A235141(8), from squared radius in the interval (4,5) to 5 results in a decrease of two due to the completion of the squares with upper right hand corner coordinates of x=1, y =2 and x=2, y=1 (since 5 = 1^2+2^2).

Links

Crossrefs

Cf. A235141, A234300, A235142, A235386.
Showing 1-3 of 3 results.

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