A277729 Irregular triangle read by rows: T(n,k) = number of times a gap of k occurs between the first n successive primes.

1, 1, 1, 1, 2, 1, 2, 0, 1, 1, 3, 0, 1, 1, 3, 0, 2, 1, 4, 0, 2, 1, 4, 0, 3, 1, 4, 0, 3, 0, 1, 1, 5, 0, 3, 0, 1, 1, 5, 0, 3, 0, 2, 1, 5, 0, 4, 0, 2, 1, 6, 0, 4, 0, 2, 1, 6, 0, 5, 0, 2, 1, 6, 0, 5, 0, 3, 1, 6, 0, 5, 0, 4, 1, 7, 0, 5, 0, 4, 1, 7, 0, 5, 0, 5, 1, 7, 0, 6, 0, 5, 1, 8, 0, 6, 0, 5, 1, 8, 0, 6, 0, 6, 1, 8, 0, 7, 0, 6, 1, 8, 0, 7, 0, 7, 1, 8, 0, 7, 0, 7, 0, 1, 1, 8, 0, 8, 0, 7, 0, 1, 1, 9, 0

Offset

2,5

Links

Robert Israel, Table of n, a(n) for n = 2..10032 (rows 2 to 410, flattened)

Example

Triangle begins:
1,
1, 1,
1, 2,
1, 2, 0, 1,
1, 3, 0, 1, <- gaps in 2,3,5,7,11,13 are 1, 2 (3 times), 4 (once)
1, 3, 0, 2,
1, 4, 0, 2,
1, 4, 0, 3,
1, 4, 0, 3, 0, 1,
1, 5, 0, 3, 0, 1,
1, 5, 0, 3, 0, 2,
1, 5, 0, 4, 0, 2,
1, 6, 0, 4, 0, 2,
1, 6, 0, 5, 0, 2,
1, 6, 0, 5, 0, 3,
1, 6, 0, 5, 0, 4,
1, 7, 0, 5, 0, 4,
1, 7, 0, 5, 0, 5,
1, 7, 0, 6, 0, 5,
1, 8, 0, 6, 0, 5,
...

Maple

N:= 30: # for rows 2 to N
res:= 1; p:= 3; R:= <1>;
for n from 2 to N do
  pp:= nextprime(p);
  d:= pp - p;
  p:= pp;
  if d <= LinearAlgebra:-Dimension(R) then
    R[d]:= R[d]+1
  else
    R(d):= 1
  fi;
  res:= res, op(convert(R, list));
od:
res;  # Robert Israel, Nov 16 2016

Crossrefs

Cf. A277730, A213930.

Sequence in context: A353328 A027414 A140083 * A057985 A135387 A321104

Adjacent sequences: A277726 A277727 A277728 * A277730 A277731 A277732

Keyword

nonn,tabf

Author

N. J. A. Sloane, Nov 06 2016

Status

approved