A009188 Short leg of more than one Pythagorean triangle.

9, 12, 15, 16, 18, 20, 21, 24, 25, 27, 28, 30, 32, 33, 35, 36, 39, 40, 42, 44, 45, 48, 49, 50, 51, 52, 54, 55, 56, 57, 60, 63, 64, 65, 66, 68, 69, 70, 72, 75, 76, 77, 78, 80, 81, 84, 85, 87, 88, 90, 91, 92, 93, 95, 96, 98, 99, 100, 102, 104, 105, 108, 110, 111, 112, 114, 115, 116

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

Values of n for which composite n X n magic squares are possible. - J. Lowell, May 20 2010

If n is in the sequence, k*n is in the sequence for all k > 1. So odd semiprimes (A046315) and numbers of the form 4*p where p is an odd prime are core subsequences which give the initial terms of arithmetic progressions in this sequence. - Altug Alkan, Nov 29 2015

Numbers appearing more than once in A009004. - Sean A. Irvine, Apr 20 2018

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001749, A009004, A020884, A046315, A264828.

Programs

Maple

filter:= proc(n) not isprime(n) and (n::odd or not isprime(n/2)) end proc:
select(filter, [$9 .. 10000]); # Robert Israel, Nov 30 2015

Mathematica

filterQ[n_] := !PrimeQ[n] && (OddQ[n] || !PrimeQ[n/2]);
Select[Range[9, 120], filterQ] (* Jean-François Alcover, Feb 28 2019, from Maple *)

PARI

forcomposite(n=9, 1e3, if(n % 2 == 1 || !isprime(n/2), print1(n, ", "))) \\ Altug Alkan, Dec 01 2015

Python

from sympy import primepi
def A009188(n):
    def f(x): return int(n+2+primepi(x)+primepi(x>>1))
    m, k = n+2, f(n+2)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Oct 17 2024

Formula

a(n) = A264828(n+2). - Chai Wah Wu, Oct 17 2024