| 数据
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29, 76, 2289, 3796, 6369, 8756, 16736, 19696, 24900, 28484, 77529, 83761, 94169, 222889, 887556, 22228889, 88875556, 112594641, 368762025, 651177616
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| 评论
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如果n d-数字,(2*n+1)*10^d+n=n*(2*10^d+1)+10^d=n^2
序列是无限的,这类数n的两个无限“族”是:
(a) n=8(k)75(k)6,2*n+1=17(k)51(k)3,n=2*6(k+1)16(k-1)7,
(b) n=2_(k+1)8_(k)9,2*n+1=4_(k
(2*n+1)//n=n^2的列表:
59//29=7^2 x 11^2,153//76=2^4 x 31^2,4579//2289=67^2 x 101^2,
7593//3796=2^2x4357^2,12739//6369=11287^2,17513//8756=2^2x13^2x509^2,
33473//16736=2^18 x 113^2,39393//19696=2^4 x 13^2 x 17^2 x 71^2,49801//24900,
56969//28484=2^2×13^2×2903^2,155059//77529=7^2×17789^2,167523//83761=347^2 x 373^2,
188339//94169=19^2 x 31^2 x 233^2,445779//222889=7^2 x 11^2 x 13^2 x 23 ^2 x 29 ^2,
1775113//887556=2^2 x 666167^2,44457779//22228889=59^2 x 73^2 x 113^2 x 137^2,
177751113//88875556=2^2 x 66661667^2,225189283//112594641=23^2 x 83^2 x 331^2 x 751^2,
737524051//368762025=5^2 x 2161^2 x 79481^2,1302355233//651177616=2^4 x 285301949^2
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