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A225082
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Centrally deletable primes.
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3
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101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 223, 229, 233, 239, 263, 269, 283, 293, 307, 311, 317, 331, 337, 347, 367, 397, 401, 421, 431, 433, 443, 457, 461, 463, 467, 487, 491, 503, 509, 523, 563
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OFFSET
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1,1
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COMMENTS
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Prime numbers that remain primes when their central digit is (or two central digits are) deleted.
At the 1886th prime number (16229), there are exactly 943 centrally deletable primes, and 943 that become composites. It appears that there are always more non-deletable primes thereafter.
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LINKS
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EXAMPLE
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a(5) = 1(1)3, and 13 is a prime.
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MATHEMATICA
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dcd[n_] := Block[{d = IntegerDigits@n, z}, z = Length@d; FromDigits@ Delete[d, Floor[(z + {{1}, {2}})/2]]]; Select[Prime@ Range@ 103, PrimeQ@ dcd@ # &] (* Giovanni Resta, Apr 29 2013 *)
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PROG
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(R) library(gmp)
sumsubstrpow<-function(n) {
no0<-function(s){ while(substr(s, 1, 1)=="0" && nchar(s)>1) s=substr(s, 2, nchar(s)); s}
tot=as.bigz(0); s=as.character(n); len=nchar(s)
for(i in 1:len) for(j in i:len) tot=tot+as.bigz(no0(substr(s, i, j)))^(j-i+1)
tot
}
#recursive
n=as.bigz(10); for(y in 1:4) n[y+1]=sumsubstrpow(n[y])
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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