A185439 Emirp gaps: Differences between consecutive emirps.

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

Metin Sariyar, Table of n, a(n) for n = 1..10000

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

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