A072822 The terms of A073215 (sums of two powers of 23) divided by 2.

1, 12, 23, 265, 276, 529, 6084, 6095, 6348, 12167, 139921, 139932, 140185, 146004, 279841, 3218172, 3218183, 3218436, 3224255, 3358092, 6436343, 74017945, 74017956, 74018209, 74024028, 74157865, 77236116, 148035889, 1702412724

Offset: 0

Author

Jeremy Gardiner, Jul 21 2002

Keywords

• nonn
• tabl
• easy

Examples

			T(2,0) = 265 = (23^2 + 23^0) / 2.
Triangle begins:
        1;
       12,      23;
      265,     276,     529;
     6084,    6095,    6348,   12167;
   139921,  139932,  140185,  146004,  279841;
  3218172, 3218183, 3218436, 3224255, 3358092, 6436343;
  ...
		

Crossrefs

Cf. A073215.

Programs

Mathematica

Union[#/2&/@(Total/@Tuples[23^Range[0,7],{2}])]  (* Harvey P. Dale, Apr 21 2011 *)

Python

from math import isqrt
def A072822(n): return 23**(a:=(k:=isqrt(m:=n<<1))+(m>k*(k+1))-1)+23**(n-1-(a*(a+1)>>1))>>1 # Chai Wah Wu, Apr 09 2025

Formula

T(n,m) = (23^n + 23^m) / 2, n = 0, 1, 2, 3 ..., m = 0, 1, 2, 3, ... n.

Extensions

Offset changed by Alois P. Heinz, Apr 09 2025