高校数学の質問スレ Part436

[過去ﾛｸﾞ] 高校数学の質問スレ Part436 (1002ﾚｽ)
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150: １３２人目の素数さん [sage] 2024/06/23(日) 19:22:52.40 ID:gsvPd9mp

＞500毎に末尾1648が現れるので
を体感

2^n 　(n>10)　の末尾4桁が1648で終わる n を100個集めて階差を算出

In[6]:= For[ans={};n=10;count=0, count<100, n++,
If[IntegerDigits[2^n][[{-4,-3,-2,-1}]]=={1,6,4,8},AppendTo[ans,n];count++]
]

In[7]:= ans

Out[7]= {131, 631, 1131, 1631, 2131, 2631, 3131, 3631, 4131, 4631, 5131, 5631, 6131, 6631, 7131,

>    7631, 8131, 8631, 9131, 9631, 10131, 10631, 11131, 11631, 12131, 12631, 13131, 13631, 14131,

>    14631, 15131, 15631, 16131, 16631, 17131, 17631, 18131, 18631, 19131, 19631, 20131, 20631,

>    21131, 21631, 22131, 22631, 23131, 23631, 24131, 24631, 25131, 25631, 26131, 26631, 27131,

>    27631, 28131, 28631, 29131, 29631, 30131, 30631, 31131, 31631, 32131, 32631, 33131, 33631,

>    34131, 34631, 35131, 35631, 36131, 36631, 37131, 37631, 38131, 38631, 39131, 39631, 40131,

>    40631, 41131, 41631, 42131, 42631, 43131, 43631, 44131, 44631, 45131, 45631, 46131, 46631,

>    47131, 47631, 48131, 48631, 49131, 49631}

In[8]:= Differences[ans]

Out[8]= {500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500,

>    500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500,

>    500, 500, 500, 500, 500}

http://rio2016.5ch.net/test/read.cgi/math/1718662026/150