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

1,1

Links

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

Example

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.

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 *)

Crossrefs

Cf. A000040, A006567.

Sequence in context: A268927 A061239 A072023 * A158723 A211116 A107288

Adjacent sequences: A217611 A217612 A217613 * A217615 A217616 A217617

Keyword

nonn,base,easy

Author

Jonathan Vos Post, Oct 08 2012

Extensions

More terms from Giovanni Resta, Oct 28 2012

Status

approved