|
%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
|
