A277730 Irregular triangle read by rows: T(n,k) = number of times a gap of 2k occurs between the first n successive odd primes.

1, 2, 2, 1, 3, 1, 3, 2, 4, 2, 4, 3, 4, 3, 1, 5, 3, 1, 5, 3, 2, 5, 4, 2, 6, 4, 2, 6, 5, 2, 6, 5, 3, 6, 5, 4, 7, 5, 4, 7, 5, 5, 7, 6, 5, 8, 6, 5, 8, 6, 6, 8, 7, 6, 8, 7, 7, 8, 7, 7, 1, 8, 8, 7, 1, 9, 8, 7, 1, 9, 9, 7, 1, 10, 9, 7, 1, 10, 10, 7, 1, 10, 10, 7, 1, 0, 0, 1, 10, 11, 7, 1, 0, 0, 1

Offset

2,2

Comments

T(m, 2) = max{T(m, k): k >= 1} for m >= 100. - Ya-Ping Lu, Dec 25 2024

Links

Lars Blomberg, Table of n, a(n) for n = 2..9997 (the first 703 rows)

Example

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

Prog

(Python)
from sympy import nextprime; p = 3; L = []
for n in range(2, 32):
    np = nextprime(p); k = (np - p)//2
    if len(L) < k: {L.append(0) for i in range(len(L), k-1)}; L.append(1)
    else: L[k-1] += 1
print(*L, sep =", ", end = ", "); p = np  # Ya-Ping Lu, Dec 25 2024

Crossrefs

Cf. A277729, A213930.

Sequence in context: A259176 A237591 A359979 * A174167 A374064 A159876

Adjacent sequences: A277727 A277728 A277729 * A277731 A277732 A277733

Keyword

nonn,look,tabf

Author

N. J. A. Sloane, Nov 06 2016

Status

approved