OFFSET
1,1
COMMENTS
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.
LINKS
Metin Sariyar, Table of n, a(n) for n = 1..10000
EXAMPLE
The first 9 emirps are 13, 17, 31, 37, 71, 73, 79, 97, 107.
Hence the first 8 gaps between consecutive emirps are:
17 - 13 = 4;
31 - 17 = 14;
37 - 31 = 6;
71 - 37 = 34;
73 - 71 = 2 (i.e., 71 and 73 are a pair of "twin prime emirps");
79 - 73 = 6;
97 - 79 = 18;
107 - 97 = 10.
So far, we see a minimum gap of 2, and a maximum of 34.
MATHEMATICA
emirpQ[n_]:=Module[{idn=IntegerDigits[n], ridn}, ridn=Reverse[idn]; idn!=ridn&&PrimeQ[FromDigits[ridn]]]
Take[Differences[Select[Prime[Range[1000]], emirpQ]], 90] (* Harvey P. Dale, Feb 18 2011 *)
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Jonathan Vos Post, Feb 03 2011
STATUS
approved