A369515 Triangle of hexagons read by row, with right diagonal having in-order odd-indexed primes, left diagonal having 2 followed by the in-order even-indexed primes, and column elements are the least multiple of the prime at the top of the column not already in the sequence, with 0 and 1 prepended.

0, 1, 2, 3, 5, 7, 4, 11, 13, 6, 10, 17, 19, 14, 8, 22, 23, 29, 26, 9, 15, 34, 31, 37, 38, 21, 12, 33, 46, 41, 43, 58, 39, 18, 20, 51, 62, 47, 53, 74, 57, 28, 16, 44, 69, 82, 59, 61, 86, 87, 52, 24, 25, 68, 93, 94, 67, 71, 106, 111, 76, 35, 30, 55, 92, 123, 118

Offset: 0

Author

J. Stauduhar, Jan 25 2024

Keywords

• nonn
• tabl

Comments

The sequence is a permutation of the nonnegative integers.

Examples

			a(0)=0, a(1)=1, followed by triangle read by rows:
                   |2|
               |3| | | |5 |
          |7 | | | |4| |  | |11|
     |13| |  | |6| | | |10| |  | |17|
|19| |  | |14| | | |8| |  | |22| |  | |23|
Row 5, element 3 = 8, because 2*3=6 has already appeared, but 2*4=8 has not.
		

Crossrefs

Cf. A143182.

Programs

Python

from sympy.ntheory.generate import prime
from math import ceil
def get_column_tops(n):
    return [1 + abs((n-1)-2*m) for m in range(1,n-1)]
def get_indices(rowNum):
  left=(rowNum*(rowNum-1))//2
  right=left+rowNum-1
  return (left, right)
def get_least(m,seq):
  mult=2
  d=m*mult
  while d in seq:
    mult+=1
    d=m*mult
  return d
seq,rnum = ([],1)
while len(seq)<56:
  seq.append(prime(rnum+max(0,rnum-2)))
  cols = get_column_tops(rnum)
  for k in range(len(cols)):
      ndcs=get_indices(cols[k])
      if k 1:
    seq.append(prime(2*rnum-1))
  rnum+=1
seq=[0,1]+seq
print(seq)