这是“雷劈数”吗

王守恩

这是“雷劈数”吗?——这是“雷劈数”！——“雷劈”——不会改变前后顺序。"数"——高位不能是"0"。——OEIS应该有这两串数。可惜没有！

100=(10-0)^2=10^2,
121=(12-1)^2=11^2,
1656369=(1656-369)^2=1287^2,
1860496=(1860-496)^2=1364^2,
123121216=(12312-1216)^2=11096^2
13967221489=(139672-21489)^2=118183^2
178659044956=(1786590-449956)^2=1336634^2
161983503471076=(16198350-3471076)^2=12727274^2
15259515629065744=(152595156-29065744)^2=123529412^2
1205042682107298321=(1205042682-107298321)^2=1097744361^2
1256370006135490884=(1256370006-135490884)^2=1120879122^2
1299640762159622884=(1299640762-159622884)^2=1140017878^2

{10, 11, 1287, 1364, 11096, 118183, 1336634, 12727274, 123529412, 1097744361, 1120879122, 1140017878, 1165991904, 1237762239, 1288553552, 1307692308, 1333666334, 1405436669, 1428571430, 1447710186, 1454545455,
Sort@Flatten@Table[(a - b) /. Solve[{10^k a + b == (a - b)^2, a > 10^k > b ≥ 10^(k - 1)}, {a, b}, Integers], {k, 9}]

81=(8+1)^2=9^2,
100=(10+0)^2=10^2,
2025=(20+25)^2=45^2,
3025=(30+25)^2=55^2,
88209=(88+209)^2=297^2,
404209=(404+209)^2=703^2,
4941729=(494+1729)^2=2223^2,
7441984=(744+1984)^2=2728^2,
24502500=(2450+2500)^2=4950^2,
25502500=(2550+2500)^2=5050^2,
52881984=(5288+1984)^2=7272^2,
60481729=(6048+1729)^2=7777^2,

{9, 10, 45, 55, 297, 703, 2223, 2728, 4950, 5050, 7272, 7777, 17344, 22222, 77778, 82656, 142857, 148149, 181819, 187110, 208495, 318682, 329967, 351352, 356643, 390313, 461539, 466830, 499500, 500500, 533170, 538461, 609687,  
Sort@Flatten@Table[(a + b) /. Solve[{10^k a + b == (a + b)^2, a > 0, b ≥ 10^(k - 1)}, {a, b},  Integers], {k, 6}]