A072822
The terms of A073215 (sums of two powers of 23) divided by 2.
Original entry on oeis.org
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
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;
...
-
Union[#/2&/@(Total/@Tuples[23^Range[0,7],{2}])] (* Harvey P. Dale, Apr 21 2011 *)
-
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
A073211
Sum of two powers of 11.
Original entry on oeis.org
2, 12, 22, 122, 132, 242, 1332, 1342, 1452, 2662, 14642, 14652, 14762, 15972, 29282, 161052, 161062, 161172, 162382, 175692, 322102, 1771562, 1771572, 1771682, 1772892, 1786202, 1932612, 3543122, 19487172, 19487182, 19487292, 19488502, 19501812, 19648222, 21258732, 38974342
Offset: 0
T(2,0) = 11^2 + 11^0 = 122.
Table T(n,m) begins:
2;
12, 22;
122, 132, 242;
1332, 1342, 1452, 2662;
14642, 14652, 14762, 15972, 29282;
...
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),
A194887 (12),
A072390 (13),
A055261 (16),
A073213 (17),
A073214 (19),
A073215 (23).
-
t = 11^Range[0, 9]; Select[Union[Flatten[Table[i + j, {i, t}, {j, t}]]], # <= t[[-1]] + 1 &] (* T. D. Noe, Oct 09 2011 *)
-
from math import isqrt
def A073211(n): return 11**(a:=(k:=isqrt(m:=n<<1))+(m>k*(k+1))-1)+11**(n-1-(a*(a+1)>>1)) # Chai Wah Wu, Apr 09 2025
A073213
Sum of two powers of 17.
Original entry on oeis.org
2, 18, 34, 290, 306, 578, 4914, 4930, 5202, 9826, 83522, 83538, 83810, 88434, 167042, 1419858, 1419874, 1420146, 1424770, 1503378, 2839714, 24137570, 24137586, 24137858, 24142482, 24221090, 25557426, 48275138, 410338674, 410338690, 410338962, 410343586, 410422194, 411758530, 434476242, 820677346
Offset: 0
T(2,0) = 17^2 + 17^0 = 290.
Table T(n,m) begins:
2;
18, 34;
290, 306, 578;
4914, 4930, 5202, 9826;
83522, 83538, 83810, 88434, 167042;
...
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),
A073214 (19),
A073215 (23).
-
Flatten[Table[Table[17^n + 17^m, {m, 0, n}], {n, 0, 7}]] (* T. D. Noe, Jun 18 2013 *)
Union[Total/@Tuples[17^Range[0,10],2]] (* Harvey P. Dale, Apr 09 2015 *)
-
from math import isqrt
def A073213(n): return 17**(a:=(k:=isqrt(m:=n<<1))+(m>k*(k+1))-1)+17**(n-1-(a*(a+1)>>1)) # Chai Wah Wu, Apr 09 2025
A073214
Sum of two powers of 19.
Original entry on oeis.org
2, 20, 38, 362, 380, 722, 6860, 6878, 7220, 13718, 130322, 130340, 130682, 137180, 260642, 2476100, 2476118, 2476460, 2482958, 2606420, 4952198, 47045882, 47045900, 47046242, 47052740, 47176202, 49521980, 94091762, 893871740, 893871758, 893872100, 893878598, 894002060, 896347838, 940917620, 1787743478
Offset: 0
T(2,0) = 19^2 + 19^0 = 362.
Table begins:
2;
20, 38;
362, 380, 722;
6860, 6878, 7220, 13718;
130322, 130340, 130682, 137180, 260642;
...
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),
A073215 (23).
-
Flatten[Table[Table[19^n + 19^m, {m, 0, n}], {n, 0, 7}]] (* T. D. Noe, Jun 18 2013 *)
Total/@Tuples[19^Range[0,10],2]//Union (* Harvey P. Dale, Jan 04 2019 *)
-
from math import isqrt
def A073214(n): return 19**(a:=(k:=isqrt(m:=n<<1))+(m>k*(k+1))-1)+19**(n-1-(a*(a+1)>>1)) # Chai Wah Wu, Apr 09 2025
Showing 1-4 of 4 results.