K-Smith numbers

liangbch

对，没有达到目的。不过这也很简单，将程序运行结果输出到文件，大约10M的数据量，然后读入内存，检测相邻的几个smith数是否连续，就可以过滤出2-smith，3-smith，乃至10-smith数了。

无心人

我想看到4以上的结果 你来帮我分析下数据吧

liangbch

在10^8以内， 4阶smith数找到38组，见下： 4463535,4463536,4463537,4463538 6356910,6356911,6356912,6356913 8188933,8188934,8188935,8188936 9425550,9425551,9425552,9425553 11148564,11148565,11148566,11148567 15966114,15966115,15966116,15966117 15966115,15966116,15966117,15966118 18542654,18542655,18542656,18542657 21673542,21673543,21673544,21673545 22821992,22821993,22821994,22821995 23767287,23767288,23767289,23767290 28605144,28605145,28605146,28605147 36615667,36615668,36615669,36615670 39227466,39227467,39227468,39227469 47096634,47096635,47096636,47096637 47395362,47395363,47395364,47395365 48072396,48072397,48072398,48072399 54054264,54054265,54054266,54054267 55464835,55464836,55464837,55464838 57484614,57484615,57484616,57484617 57756450,57756451,57756452,57756453 57761165,57761166,57761167,57761168 58418508,58418509,58418510,58418511 61843387,61843388,61843389,61843390 62577157,62577158,62577159,62577160 64572186,64572187,64572188,64572189 65484066,65484067,65484068,65484069 66878432,66878433,66878434,66878435 67118680,67118681,67118682,67118683 71845857,71845858,71845859,71845860 75457380,75457381,75457382,75457383 75457381,75457382,75457383,75457384 77247606,77247607,77247608,77247609 78432168,78432169,78432170,78432171 88099213,88099214,88099215,88099216 89653781,89653782,89653783,89653784 90166567,90166568,90166569,90166570 92656434,92656435,92656436,92656437 在10^8以内，5阶smith数只找到 2组，见下。而5阶以上的smith数，则没有发现。 15966114,15966115,15966116,15966117,15966118 75457380,75457381,75457382,75457383,75457384

liangbch

重新计算到10^9, 4阶smith数达到384个，而5阶smith数也达到14个，见下。而5阶以上smith数则依然没有发现。

1. 15966114,15966115,15966116,15966117,15966118
2. 75457380,75457381,75457382,75457383,75457384
3. 162449165,162449166,162449167,162449168,162449169
4. 296049306,296049307,296049308,296049309,296049310
5. 296861735,296861736,296861737,296861738,296861739
6. 334792990,334792991,334792992,334792993,334792994
7. 429619207,429619208,429619209,429619210,429619211
8. 581097690,581097691,581097692,581097693,581097694
9. 581519244,581519245,581519246,581519247,581519248
10. 582548088,582548089,582548090,582548091,582548092
11. 683474015,683474016,683474017,683474018,683474019
12. 809079150,809079151,809079152,809079153,809079154
13. 971285861,971285862,971285863,971285864,971285865
14. 977218716,977218717,977218718,977218719,977218720

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liangbch

http://www.shyamsundergupta.com/smith.htm 说，最小的6连续smith数是2050918644, 2050918645, 2050918646, 2050918647, 2050918648, 2050918649。

If there are k consecutive numbers which are Smith numbers, these can be termed as k-consecutive Smith numbers. The smallest set of 6-consecutive smith numbers is (2050918644, 2050918645, 2050918646, 2050918647, 2050918648, 2050918649). This is the only set of 6-consecutive smith numbers below 1010. There is no set of higher consecutive smith numbers below 1010. Can you find the smallest set of 7-consecutive smith numbers ?.

medie2005

7-Smith numbers 164736913905=3*3*5*257*14244437 (dig_sum=54) 164736913906=2*61*109*139*89123 (dig_sum=55) 164736913907=31*31*2293*74759 (dig_sum=56) 164736913908=2*2*3*7*1961153737 (dig_sum=57) 164736913909=3947*41737247 (dig_sum=58) 164736913910=2*5*19*41*21147229 (dig_sum=50) 164736913911=3*293*187414009 (dig_sum=51)

liangbch

7连续smith数你是怎么得到的，自己编程序算的吗？如果是，你的程序相对于我的程序效率如何？

medie2005

见primepuzzle 247.末尾有如下文字： J. K. Andersen wrote (April 08): Q1) The seventh term of A059754 is 164736913905; the first start of 7 consecutive Smith numbers.

liangbch

按照我程序的速度，大约在13个小时后就可以搜索到这个7-smith数。

medie2005

呵呵，那只要你肯花时间，应该可以找到8-smith numbers。