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

Author

Jonathan Vos Post, Feb 03 2011

Keywords

• nonn
• base
• easy

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A000040, A000101, A001223, A002386, A006567.

Programs

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 *)

Formula

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