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

Offset: 1

Author

Kevin L. Schwartz and Christian N. K. Anderson, Apr 26 2013

Keywords

• nonn
• base

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.

Examples

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

Links

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

Crossrefs

Cf. A080603, A077359

Programs

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 *)

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])