A185439 - OEIS

%I #22 Mar 04 2020 21:19:37

%S 4,14,6,34,2,6,18,10,6,36,8,10,12,20,112,26,10,12,30,312,8,24,6,4,8,

%T 10,8,138,30,4,12,14,4,12,8,18,12,10,2,28,8,22,6,6,6,42,2,28,12,8,12,

%U 4,6,6,2,6,12,10,20,4,18,20,60,18,10,20,10,14,18,16,12,12,12,36,24,14,4,18,38,12,54,10,8,12,36,22,20

%N Emirp gaps: Differences between consecutive emirps.

%C Gaps between consecutive primes whose reversal is a different prime. This is to Differences between consecutive primes (A001223) as emirps (A006567) are to primes (A000040). This was indirectly suggested to me in a facebook conversation with _Kevin L. Schwartz_. One may use this to derive other sequences: records in emirp gaps; lower of pair of consecutive emirps with record gap; larger of pair of emirps with record gaps, by analogy with A005250, A002386, A000101.

%H Metin Sariyar, <a href="/A185439/b185439.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A006567(n+1) - A006567(n).

%e The first 9 emirps are 13, 17, 31, 37, 71, 73, 79, 97, 107.

%e Hence the first 8 gaps between consecutive emirps are:

%e    17 - 13 =  4;

%e    31 - 17 = 14;

%e    37 - 31 =  6;

%e    71 - 37 = 34;

%e    73 - 71 =  2 (i.e., 71 and 73 are a pair of "twin prime emirps");

%e    79 - 73 =  6;

%e    97 - 79 = 18;

%e   107 - 97 = 10.

%e So far, we see a minimum gap of 2, and a maximum of 34.

%t emirpQ[n_]:=Module[{idn=IntegerDigits[n],ridn},ridn=Reverse[idn];idn!=ridn&&PrimeQ[FromDigits[ridn]]]

%t Take[Differences[Select[Prime[Range[1000]],emirpQ]],90]  (* _Harvey P. Dale_, Feb 18 2011 *)

%Y Cf. A000040, A000101, A001223, A002386, A006567.

%K nonn,base,easy

%O 1,1

%A _Jonathan Vos Post_, Feb 03 2011