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A185439 Emirp gaps: Differences between consecutive emirps.

%I A185439 #22 Mar 04 2020 21:19:37
%S A185439 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 A185439 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 A185439 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 A185439 Emirp gaps: Differences between consecutive emirps.
%C A185439 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 A185439 Metin Sariyar, <a href="/A185439/b185439.txt">Table of n, a(n) for n = 1..10000</a>
%F A185439 a(n) = A006567(n+1) - A006567(n).
%e A185439 The first 9 emirps are 13, 17, 31, 37, 71, 73, 79, 97, 107.
%e A185439 Hence the first 8 gaps between consecutive emirps are:
%e A185439    17 - 13 =  4;
%e A185439    31 - 17 = 14;
%e A185439    37 - 31 =  6;
%e A185439    71 - 37 = 34;
%e A185439    73 - 71 =  2 (i.e., 71 and 73 are a pair of "twin prime emirps");
%e A185439    79 - 73 =  6;
%e A185439    97 - 79 = 18;
%e A185439   107 - 97 = 10.
%e A185439 So far, we see a minimum gap of 2, and a maximum of 34.
%t A185439 emirpQ[n_]:=Module[{idn=IntegerDigits[n],ridn},ridn=Reverse[idn];idn!=ridn&&PrimeQ[FromDigits[ridn]]]
%t A185439 Take[Differences[Select[Prime[Range[1000]],emirpQ]],90]  (* _Harvey P. Dale_, Feb 18 2011 *)
%Y A185439 Cf. A000040, A000101, A001223, A002386, A006567.
%K A185439 nonn,base,easy
%O A185439 1,1
%A A185439 _Jonathan Vos Post_, Feb 03 2011