A217614 Emirps p such that the next emirp is equal to the next prime.

13, 31, 71, 73, 337, 701, 733, 739, 743, 761, 937, 953, 967, 983, 1021, 1031, 1097, 1103, 1151, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1279, 1381, 1399, 1499, 1511, 1583, 1597, 1723, 1733, 1831, 1933, 3011, 3019, 3083, 3089, 3191, 3271, 3299

Offset: 1

Author

Jonathan Vos Post, Oct 08 2012

Keywords

• nonn
• base
• easy

Examples

			13 is in the sequence because the next emirp (17) is also the next prime.
71 is in the sequence because the next emirp (73) is also the next prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A006567.

Programs

Maple

digrev:= proc(n) local L,i;
 L:= convert(n,base,10);
 add(L[-i]*10^(i-1),i=1..nops(L))
end proc:
isemirp:= proc(n) local r;
  r:= digrev(n);
  r <> n and isprime(r)
end proc:
R:= NULL: count:= 0:
p:= 2: ep:= false:
while count < 100 do
  q:= p; eq:= ep;
  p:= nextprime(p);
  ep:= isemirp(p);
  if ep and eq then
     R:= R, q; count:= count+1;
  fi
od:
R; # Robert Israel, Jun 20 2021

Mathematica

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

Extensions

More terms from Giovanni Resta, Oct 28 2012