A213930 Table of frequencies of gaps of size 2d between consecutive primes below 10^n, n >= 1; d = 1,2,...,A213949(n).

2, 8, 7, 7, 1, 35, 40, 44, 15, 16, 7, 7, 0, 1, 1, 205, 202, 299, 101, 119, 105, 54, 33, 40, 15, 16, 15, 3, 5, 11, 1, 2, 1, 1224, 1215, 1940, 773, 916, 964, 484, 339, 514, 238, 223, 206, 88, 98, 146, 32, 33, 54, 19, 28, 19, 5, 4, 3, 5

Offset

1,1

Comments

Sum of elements in line n is Pi(10^n)-2. Column d is the sequence of the numbers of gaps of size 2d between consecutive primes up to 10^n. For example, column 1 is A007508, and column 2 is A093737. Column 3 corresponds to the jumping champion 6. Column 15 corresponds to the next champion 30. It is interesting that local maximums appear in the beginning of this column, 11 in line 4, and 146 in line 5.

Links

Washington Bomfim, Rows n = 1..13, flattened

A. Odlyzko, M. Rubinstein and M. Wolf, Jumping Champions

Index entries for primes, gaps between

Example

Table begins
   2
   8    7    7   1
  35   40   44  15  16   7   7   0   1   1
  205  202  299 101 119 105  54  33  40  15  16  15  3  5  11  1  2  1
1224 1215 1940 773 916 964 484 339 514 238 223 206 88 98 146 32 33 54 19 28...

Mathematica

Table[t2 = Sort[Tally[Table[Prime[k + 1] - Prime[k], {k, 2, PrimePi[10^n] - 1}]]]; maxDiff = t2[[-1, 1]]/2; t3 = Table[0, {k, maxDiff}]; Do[t3[[t2[[i, 1]]/2]] = t2[[i, 2]], {i, Length[t2]}]; t3, {n, 5}] (* T. D. Noe, Jun 25 2012 *)

Crossrefs

Cf. A038460, A000720, A007508, A093737, A213949 (row lengths).

Sequence in context: A202693 A174552 A083679 * A319463 A079031 A203145

Adjacent sequences: A213927 A213928 A213929 * A213931 A213932 A213933

Keyword

tabf,nonn,nice

Author

Washington Bomfim, Jun 24 2012

Status

approved