

A185439


Emirp gaps. Differences between consecutive emirps.


1



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
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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

Table of n, a(n) for n=1..87.


FORMULA

a(n) = A006567(n+1)  A006567(n).


EXAMPLE

Here are the first 9 emirps:
13, 17, 31, 37, 71, 73, 79, 97, 107.
Hence the first 8 gaps between consecutive emirps are:
(1713) = 4.
(3117) = 14.
(3731) = 6.
(7137) = 34.
(7371) = 2 (i.e. 71 and 73 are a pair of "twin prime emirps")
(7973) = 6.
(9779) = 18.
(10797) = 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

Cf. A000040, A000101, A001223, A002386, A006567.
Sequence in context: A131702 A276826 A029661 * A304458 A133856 A018853
Adjacent sequences: A185436 A185437 A185438 * A185440 A185441 A185442


KEYWORD

nonn,base,easy


AUTHOR

Jonathan Vos Post, Feb 03 2011


STATUS

approved



