A217614 - OEIS

%I #23 Jun 20 2021 17:25:20

%S 13,31,71,73,337,701,733,739,743,761,937,953,967,983,1021,1031,1097,

%T 1103,1151,1193,1201,1213,1217,1223,1229,1231,1237,1249,1279,1381,

%U 1399,1499,1511,1583,1597,1723,1733,1831,1933,3011,3019,3083,3089,3191,3271,3299

%N Emirps p such that the next emirp is equal to the next prime.

%H Robert Israel, <a href="/A217614/b217614.txt">Table of n, a(n) for n = 1..10000</a>

%e 13 is in the sequence because the next emirp (17) is also the next prime.

%e 71 is in the sequence because the next emirp (73) is also the next prime.

%p digrev:= proc(n) local L,i;

%p  L:= convert(n,base,10);

%p  add(L[-i]*10^(i-1),i=1..nops(L))

%p end proc:

%p isemirp:= proc(n) local r;

%p   r:= digrev(n);

%p   r <> n and isprime(r)

%p end proc:

%p R:= NULL: count:= 0:

%p p:= 2: ep:= false:

%p while count < 100 do

%p   q:= p; eq:= ep;

%p   p:= nextprime(p);

%p   ep:= isemirp(p);

%p   if ep and eq then

%p      R:= R, q; count:= count+1;

%p   fi

%p od:

%p R; # _Robert Israel_, Jun 20 2021

%t emirpQ[n_] := PrimeQ[n] && Block[{r=FromDigits@Reverse@IntegerDigits@n},

%t r != n && PrimeQ[r]]; nextEmirp[n_] := Block[{e=NextPrime[n]}, While[! emirpQ[e], e = NextPrime[e]]; e]; Select[Prime@Range@1000, emirpQ[#] && NextPrime[#] == nextEmirp[#] &] (* _Giovanni Resta_, Oct 28 2012 *)

%Y Cf. A000040, A006567.

%K nonn,base,easy

%O 1,1

%A _Jonathan Vos Post_, Oct 08 2012

%E More terms from _Giovanni Resta_, Oct 28 2012