A072390 Sum of two powers of 13.

2, 14, 26, 170, 182, 338, 2198, 2210, 2366, 4394, 28562, 28574, 28730, 30758, 57122, 371294, 371306, 371462, 373490, 399854, 742586, 4826810, 4826822, 4826978, 4829006, 4855370, 5198102, 9653618, 62748518, 62748530, 62748686, 62750714, 62777078, 63119810, 67575326, 125497034

Offset: 0

Author

Jeremy Gardiner, Jul 20 2002

Keywords

• easy
• nonn
• tabl

Links

• T. D. Noe, Rows n = 0..100 of triangle, flattened

Programs

Mathematica

Union[Total/@Tuples[13^Range[0,9], 2]] (* Harvey P. Dale, Sep 15 2011 *)
Flatten[Table[Table[13^n + 13^m, {m, 0, n}], {n, 0, 10}]] (* T. D. Noe, Jun 18 2013 *)

Python

def aupto(lim):
  pows, p = [], 1
  while p < lim: pows.append(p); p *= 13
  return sorted([a+b for a in pows for b in pows if b >= a and a+b <= lim])
print(aupto(63119810)) # Michael S. Branicky, Feb 14 2021

Python

from math import isqrt
def A072390(n): return 13**(a:=(k:=isqrt(m:=n<<1))+(m>k*(k+1))-1)+13**(n-1-(a*(a+1)>>1)) # Chai Wah Wu, Apr 08 2025

Formula

T(n,m) = 13^n + 13^m, n = 0, 1, 2, 3 ..., m = 0, 1, 2, 3, ... n.