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A277729 Irregular triangle read by rows: T(n,k) = number of times a gap of k occurs between the first n successive primes. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A035160 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

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Last modified December 8 11:31 EST 2021. Contains 349596 sequences. (Running on oeis4.)