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Centrally deletable primes.
4

%I #12 Apr 30 2013 12:02:25

%S 101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,

%T 191,193,197,199,223,229,233,239,263,269,283,293,307,311,317,331,337,

%U 347,367,397,401,421,431,433,443,457,461,463,467,487,491,503,509,523,563

%N Centrally deletable primes.

%C Prime numbers that remain primes when their central digit is (or two central digits are) deleted.

%C 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.

%C Subset of A080603 and of A077359.

%H Christian N. K. Anderson, <a href="/A225082/b225082.txt">Table of n, a(n) for n = 1..10000</a>

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

%t 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 *)

%o (R) library(gmp)

%o sumsubstrpow<-function(n) {

%o no0<-function(s){ while(substr(s,1,1)=="0" && nchar(s)>1) s=substr(s,2,nchar(s)); s}

%o tot=as.bigz(0); s=as.character(n); len=nchar(s)

%o for(i in 1:len) for(j in i:len) tot=tot+as.bigz(no0(substr(s,i,j)))^(j-i+1)

%o tot

%o }

%o #recursive

%o n=as.bigz(10); for(y in 1:4) n[y+1]=sumsubstrpow(n[y])

%Y Cf. A080603, A077359

%K nonn,base

%O 1,1

%A _Kevin L. Schwartz_ and _Christian N. K. Anderson_, Apr 26 2013