A349191 a(n) = A000720(A348907(n+1)).

1, 2, 1, 3, 2, 4, 1, 3, 2, 5, 4, 6, 1, 3, 2, 7, 5, 8, 4, 6, 1, 9, 3, 2, 7, 5, 8, 10, 4, 11, 6, 1, 9, 3, 2, 12, 7, 5, 8, 13, 10, 14, 4, 11, 6, 15, 1, 9, 3, 2, 12, 16, 7, 5, 8, 13, 10, 17, 14, 18, 4, 11, 6, 15, 1, 19, 9, 3, 2, 20, 12, 21, 16, 7, 5, 8, 13, 22, 10

Offset: 1

Author

Michael De Vlieger, Nov 09 2021

Keywords

• nonn
• easy

Comments

Regarding this sequence as an irregular triangle T(m,j) where the rows m terminate with 1 exhibits row length A338237(m). In such rows m, we have a permutation of the range of natural numbers 1..A338237(m).

Records are the natural numbers.

Examples

			Table showing a(n) for the first rows m of this sequence seen as an irregular triangle T(m,j). "New" numbers introduced for prime (n+1) are shown in parentheses:
  m\j   1   2   3   4   5   6   7   8   9  10  11   A338237(m)
  ------------------------------------------------------------
  1:   (1)                                                1
  2:   (2)  1                                             2
  3:   (3)  2  (4)  1                                     4
  4:    3   2  (5)  4  (6)  1                             6
  5:    3   2  (7)  5  (8)  4   6   1                     8
  6:   (9)  3   2   7   5   8 (10)  4 (11)  6   1        11
  ...
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10237 (as an irregular triangle, rows 1 <= n <= 36, flattened)
• Michael De Vlieger, Log-log scatterplot of a(n) for 1 <= n <= 11636, showing 36 rows if read as an irregular table.

Crossrefs

Cf. A000027, A000040, A000720, A338237, A348907, A349192.

Programs

Mathematica

c = 0; 1 + Reap[Do[Set[a[i], If[PrimeQ[i], i; c++, a[i - c]] ]; Sow[a[i]], {i, 2, 2^24}] ][[-1, -1]]