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A348907 If n is prime, a(n) = n, else a(n) = a(n-pi(n)), n >= 2; where pi is the prime counting function A000720.

%I A348907 #42 Nov 10 2021 01:16:27
%S A348907 2,3,2,5,3,7,2,5,3,11,7,13,2,5,3,17,11,19,7,13,2,23,5,3,17,11,19,29,7,
%T A348907 31,13,2,23,5,3,37,17,11,19,41,29,43,7,31,13,47,2,23,5,3,37,53,17,11,
%U A348907 19,41,29,59,43,61,7,31,13,47,2,67,23,5,3,71,37,73,53,17,11
%N A348907 If n is prime, a(n) = n, else a(n) = a(n-pi(n)), n >= 2; where pi is the prime counting function A000720.
%C A348907 A fractal sequence in which every term is prime. The proper subsequence a(k), for composite numbers k = 4,6,8,9... is identical to the original, and the records subsequence is A000040.
%C A348907 Regarding this sequence as an irregular triangle T(m,j) where the rows m terminate with 2 exhibits row length A338237(m). In such rows m, we have a permutation of the least A338237(m) primes. - _Michael De Vlieger_, Nov 04 2021
%H A348907 Michael De Vlieger, <a href="/A348907/b348907.txt">Table of n, a(n) for n = 2..10238</a> (as an irregular triangle, rows 1 <= n <= 35 flattened).
%H A348907 Michael De Vlieger, <a href="/A348907/a348907.png">Log-log scatterplot of a(n)</a>, for n=1..2^16.
%e A348907 2 is prime so a(2) = 2.
%e A348907 3 is prime so a(3) = 3.
%e A348907 4 is not prime so a(4) = a(4-pi(4)) = 2.
%e A348907 5 is prime so a(5) = 5.
%e A348907 6 is composite so a(6) = a(6-pi(6)) = 3.
%e A348907 From _Michael De Vlieger_, Nov 04 2021: (Start)
%e A348907 Table showing pi(a(n)) for the first rows m of this sequence seen as an irregular triangle T(m,j). "New" primes introduced for prime n are shown in parentheses:
%e A348907 m\j   1   2   3   4   5   6   7   8   9  10  11   A338237(m)
%e A348907 ------------------------------------------------------------
%e A348907 1:   (1)                                                1
%e A348907 2:   (2)  1                                             2
%e A348907 3:   (3)  2  (4)  1                                     4
%e A348907 4:    3   2  (5)  4  (6)  1                             6
%e A348907 5:    3   2  (7)  5  (8)  4   6   1                     8
%e A348907 6:   (9)  3   2   7   5   8 (10)  4 (11)  6   1        11
%e A348907 ... (End)
%t A348907 a[n_]:=If[PrimeQ@n,n,a[n-PrimePi@n]];Array[a,75,2] (* _Giorgos Kalogeropoulos_, Nov 03 2021 *)
%o A348907 (PARI) a(n) = if (isprime(n), n, a(n-primepi(n))); \\ _Michel Marcus_, Nov 03 2021
%o A348907 (Python)
%o A348907 from sympy import isprime
%o A348907 def aupton(nn):
%o A348907     alst, primepi = [], 0
%o A348907     for n in range(2, nn+1):
%o A348907         if isprime(n): an, primepi = n, primepi + 1
%o A348907         else: an = alst[n - primepi - 2]
%o A348907         alst.append(an)
%o A348907     return alst
%o A348907 print(aupton(76)) # _Michael S. Branicky_, Nov 04 2021
%Y A348907 Cf. A000040, A002808, A000720, A010051, A338237.
%K A348907 nonn,look
%O A348907 2,1
%A A348907 _David James Sycamore_, Nov 03 2021
%E A348907 More terms from _Michel Marcus_, Nov 03 2021