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A185439
Emirp gaps: Differences between consecutive emirps.
3
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, 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, 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
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
FORMULA
a(n) = A006567(n+1) - A006567(n).
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