A224954 Numbers n such that a positive number m < n exists such that n-m, n+m, and n*m are oblong numbers (A002378).

42, 146, 2850, 9074, 13464, 17640, 20502, 32406, 53892, 55352, 59124, 229284, 340890, 344904, 507012, 562466, 1016076, 1958082, 3938256, 6087890, 6924960, 7645106, 8070342, 11694540, 11861892, 12721884, 12960020, 15959802, 18999750, 34863842, 40503060, 42000420, 55377282

Offset

1,1

Comments

Sequence of corresponding m's begins: 30, 36, 1980, 2268, 11658, 16770, 3990, 900, 14490, 54540, ...

Conjectures:

1. The sequence is infinite.

2. There is only one m for each n (this is true for n < 2^26).

Links

Kevin P. Thompson, Table of n, a(n) for n = 1..77

Prog

(Java)
public class A224954 {
  public static long sr0 = 1;
  public static boolean[] Oblong = new boolean[1 << 27];
  public static boolean isOblong(long a) {
    long b, s, sr = sr0;
    while (a < sr*(sr+1))  sr>>=1;
    b = sr>>1;
    while (b!=0) {
        s = sr+b;
        if (a >= s*(s+1))  sr = s;
        b>>=1;
    }
    if (a == sr*(sr+1))  return true;
    return false;
  }
  public static void main (String[] args) {
    for (int i = 0; i*(i+1) < (1 << 27); ++i)  Oblong[i*(i+1)] = true;
    for (long a = 0; a < (1 << 26); a+=2) {
      long s = 1L << 30, obn = 0, count = 0, lastB = 0;
      while (a*a < s*(s+1))  s>>=1;
      sr0 = s;
      for (long i = 2; obn < a; i+=2) {
        long b = a - obn;
        if (Oblong[(int)(a*2-obn)])
          if (isOblong(a*(a-obn)))  { ++count; lastB = b; }
        obn += i;
      }
      if (count!=0)  System.out.printf("\n%d %d  %d ", a, lastB, count);
      if ((a & 0x3fff)==0)  System.out.printf(".");
    }
  }
}

Crossrefs

Cf. A002378, A224935.

Sequence in context: A044755 A262424 A230932 * A299131 A158479 A188126

Adjacent sequences: A224951 A224952 A224953 * A224955 A224956 A224957

Keyword

nonn

Author

Alex Ratushnyak, Apr 20 2013

Status

approved