[seqfan] A (not triangular) array inspired by A083197

Eric Angelini Eric.Angelini at kntv.be
Mon Apr 8 15:14:23 CEST 2013


Hello SeqFans,

http://oeis.org/A083197
... has given me the idea of a variation. Here is A083197:

> Triangular array, read by rows, where 
  if n is odd the n-th row consists of n least unused non-primes, while 
  if n is even the n-th row consists of the n least unused primes.

  Triangle begins:
  1
  2 3
  4 6 8
  5 7 11 13
  9 10 12 14 15
  17 19 23 29 31 37
  etc.
  -----------------

... In this variation the size of each row is given by the successive
integers of the sequence itself, not by n. Thus the array would begin:

                                    row size
  1                                     1    (non-prime)
  2 3                                   2    (primes)
  4 6 8                                 3    (non-primes)
  5 7 11 13                             4    (primes)
  9 10 12 14 15 16                      6    (non-primes)
  17 19 23 29 31 37 41 43               8    (primes)
  18 20 21 22 24                        5    (non-primes)
  47 51 53 59 61 67 71                  7    (primes)
  25 26 27 28 30 32 33 34 35 36 38     11    (non-primes)
  ...

As A083197, this new seq is of course a permutation of the natural numbers.

Best,
É.



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