A037168 -id:A037168 - cp's OEIS frontend

A114557 a(2n-1) = 2*(p-1) and a(2n) = p + 3, where p=prime(n).

2, 5, 4, 6, 8, 8, 12, 10, 20, 14, 24, 16, 32, 20, 36, 22, 44, 26, 56, 32, 60, 34, 72, 40, 80, 44, 84, 46, 92, 50, 104, 56, 116, 62, 120, 64, 132, 70, 140, 74, 144, 76, 156, 82, 164, 86, 176, 92, 192, 100, 200, 104, 204, 106, 212, 110, 216, 112, 224, 116, 252, 130, 260, 134

Offset: 1

Roger L. Bagula, Feb 15 2006

G. C. Greubel, Table of n, a(n) for n = 1..10000

[((3-(-1)^n)*NthPrime(Floor((n+1)/2)) + (1+5*(-1)^n))/2: n in [1..70]]; // G. C. Greubel, May 20 2019

Flatten[Table[Abs[Coefficient[Expand[(x+2)(x -(1 +Sqrt[Prime[n]]))*(x - (1 - Sqrt[Prime[n]]))], x, m]], {n, 1, 50}, {m, 0, 1}]]
With[{p = Prime[Floor[(n+1)/2]]}, Table[If[OddQ[n], 2*(p-1), p+3], {n, 1, 70}]] (* G. C. Greubel, May 20 2019 *)

{a(n) = ((3-(-1)^n)*prime(floor((n+1)/2)) + (1+5*(-1)^n))/2}; \\ G. C. Greubel, May 20 2019

[( (3-(-1)^n)*nth_prime(floor((n+1)/2))+ (1+5*(-1)^n))/2 for n in (1..70)] # G. C. Greubel, May 20 2019

a(2n-1) = A037168(n). a(2n) = A113935(n).

a(n) = ( (3 - (-1)^n)*prime(floor((n+1)/2)) + (1 + 5*(-1)^n) )/2. - G. C. Greubel, May 20 2019

A369497 Table read by rows: row n is the unique primitive Pythagorean triple (a,b,c) such that (a-b+c)/2 = prime(n+2) and whose short leg "a" is even.

Original entry on oeis.org

8, 15, 17, 12, 35, 37, 20, 99, 101, 24, 143, 145, 32, 255, 257, 36, 323, 325, 44, 483, 485, 56, 783, 785, 60, 899, 901, 72, 1295, 1297, 80, 1599, 1601, 84, 1763, 1765, 92, 2115, 2117, 104, 2703, 2705, 116, 3363, 3365, 120, 3599, 3601, 132, 4355, 4357, 140, 4899, 4901, 144, 5183, 5185, 156, 6083, 6085

Offset: 1

Miguel-Ángel Pérez García-Ortega, Jan 24 2024

See Exercise 3.5 of the reference.

			Table begins:
  n=1:   8,  15,  17;
  n=2:  12,  35,  37;
  n=3:  20,  99, 101;
  n=4:  24, 143, 145;
  n=5:  32, 255, 257;

Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2024.

Miguel-Ángel Pérez García-Ortega, Ejercicio 3.5.

Cf. A037168 (short leg), A040976 (inradius).

Row n = (a, b, c) = (2*p - 2, p^2 - 2*p, p^2 - 2*p + 2), where p = prime(n+2) = A000040(n+2).

cp's OEIS Frontend

A114557 a(2n-1) = 2*(p-1) and a(2n) = p + 3, where p=prime(n).

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A369497 Table read by rows: row n is the unique primitive Pythagorean triple (a,b,c) such that (a-b+c)/2 = prime(n+2) and whose short leg "a" is even.

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