A073215 Sum of two powers of 23.

2, 24, 46, 530, 552, 1058, 12168, 12190, 12696, 24334, 279842, 279864, 280370, 292008, 559682, 6436344, 6436366, 6436872, 6448510, 6716184, 12872686, 148035890, 148035912, 148036418, 148048056, 148315730, 154472232, 296071778

Offset: 0

Author

Jeremy Gardiner, Jul 20 2002

Keywords

• easy
• nonn
• tabl

Examples

			T(2,0) = 23^2 + 23^0 = 530.
Table begins:
       2;
      24,     46;
     530,    552,   1058;
   12168,  12190,  12696,  24334;
  279842, 279864, 280370, 292008, 559682;
  ...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..999 [Offset changed to 0 by _Georg Fischer_, Mar 01 2022]

Crossrefs

Cf. A009967.

Equals twice A072822.

Sums of two powers of n: A073423 (0), A007395 (1), A173786 (2), A055235 (3), A055236 (4), A055237 (5), A055257 (6), A055258 (7), A055259 (8), A055260 (9), A052216 (10), A073211 (11), A194887 (12), A072390 (13), A055261 (16), A073213 (17), A073214 (19).

Programs

Mathematica

With[{nn=30},Take[Union[Total/@Tuples[23^Range[0,nn],2]],nn]] (* Harvey P. Dale, Oct 16 2017 *)

Python

from math import isqrt
def A073215(n): return 23**(a:=(k:=isqrt(m:=n<<1))+(m>k*(k+1))-1)+23**(n-1-(a*(a+1)>>1)) # Chai Wah Wu, Apr 09 2025

Formula

T(n, m) = 23^n + 23^m, for n >= 0 and m in [0..n].

Bivariate g.f.: (2 - 24*x) / ((1 - x) * (1 - 23*x) * (1 - 23*x*y)). - J. Douglas Morrison, Jul 29 2021