A152738 -id:A152738 - cp's OEIS frontend

A153287 First differences of A152738.

0, 2, 3, 4, 6, 7, 8, 9, 11, 11, 13, 14, 16, 17, 18, 19, 20, 22, 23, 24, 25, 27, 27, 29, 31, 31, 33, 34, 35, 37, 37, 39, 41, 41, 43, 43, 46, 46, 48, 48, 50, 52, 52, 54, 55, 56, 58, 58, 60, 62, 62, 64, 65, 66, 67, 69, 69, 72, 72, 73, 75, 76, 77, 79, 80, 81, 82, 83, 85, 86, 87, 88, 90, 91

Offset: 0

Paul Curtz, Dec 23 2008

nonn

B. D. Swan, Table of n, a(n) for n=0,...,10000

A293407 Least integer k such that k/n^2 > (-1 + sqrt(5))/2 (the golden ratio).

Original entry on oeis.org

0, 1, 3, 6, 10, 16, 23, 31, 40, 51, 62, 75, 89, 105, 122, 140, 159, 179, 201, 224, 248, 273, 300, 327, 356, 387, 418, 451, 485, 520, 557, 594, 633, 674, 715, 758, 801, 847, 893, 941, 989, 1039, 1091, 1143, 1197, 1252, 1308, 1366, 1424, 1484, 1546, 1608, 1672

Offset: 0

Clark Kimberling, Oct 11 2017

Clark Kimberling, Table of n, a(n) for n = 0..1000

Cf. A001622, A293401, A293403, A152738, A293408.

z = 120; r = -1+GoldenRatio;
Table[Floor[r*n^2], {n, 0, z}];   (* A152738 *)
Table[Ceiling[r*n^2], {n, 0, z}]; (* A293407 *)
Table[Round[r*n^2], {n, 0, z}];   (* A293408 *)

a(n) = ceiling(r*n^2), where r = (-1 + sqrt(5))/2.

a(n) = A152738(n) + 1 for n > 0.

A293408 The integer k that minimizes |k/n^2 - 1/tau|, where tau = (1+sqrt(5))/2 (golden ratio).

Original entry on oeis.org

0, 1, 2, 6, 10, 15, 22, 30, 40, 50, 62, 75, 89, 104, 121, 139, 158, 179, 200, 223, 247, 273, 299, 327, 356, 386, 418, 451, 485, 520, 556, 594, 633, 673, 714, 757, 801, 846, 892, 940, 989, 1039, 1090, 1143, 1197, 1252, 1308, 1365, 1424, 1484, 1545, 1608, 1671

Offset: 0

Clark Kimberling, Oct 11 2017

Clark Kimberling, Table of n, a(n) for n = 0..1000

Cf. A001622, A293402, A293404, A152738, A293407.

z = 120; r = -11+GoldenRatio;
Table[Floor[r*n^2], {n, 0, z}];   (* A152738 *)
Table[Ceiling[r*n^2], {n, 0, z}]; (* A293407 *)
Table[Round[r*n^2], {n, 0, z}];   (* A293408 *)

a(n) = floor(1/2 + (n^2)/tau).

a(n) = A152738(n) if (fractional part of (1/tau)*n^2) < 1/2, else a(n) = A293407(n).

cp's OEIS Frontend

A153287 First differences of A152738.

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A293407 Least integer k such that k/n^2 > (-1 + sqrt(5))/2 (the golden ratio).

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A293408 The integer k that minimizes |k/n^2 - 1/tau|, where tau = (1+sqrt(5))/2 (golden ratio).

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Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula