A225082 - OEIS

A225082

Centrally deletable primes.

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

1,1

COMMENTS

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.

Subset of A080603 and of A077359.

LINKS

Christian N. K. Anderson, Table of n, a(n) for n = 1..10000

EXAMPLE

a(5) = 1(1)3, and 13 is a prime.

MATHEMATICA

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 *)

PROG

(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])

CROSSREFS

Cf. A080603, A077359