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A353731 a(n) = index where prime(n) appears in A352808.

%I A353731 #16 May 18 2022 07:57:42
%S A353731 2,6,4,11,18,19,16,24,45,52,63,29,30,78,122,71,123,148,46,72,53,162,
%T A353731 96,66,100,161,243,212,194,186,394,75,86,110,114,177,204,111,254,295,
%U A353731 273,274,494,124,167,386,338,642,339,410,347,650,351,762,159,180,195,250,191,208,225,270,284,595,340,689,290,238,732,730,258,651,696,624,749,1062,271,311,300,326,666,625,1006,634,1007,1050,269,738,759,970,898,1443,1122,1123,1139,1570,1483
%N A353731 a(n) = index where prime(n) appears in A352808.
%C A353731 Here prime(n) means the n-th prime in 2, 3, 5, 7, ..., not the n-th term of A352808 that happens to be a prime.
%H A353731 Michael S. Branicky, <a href="/A353731/b353731.txt">Table of n, a(n) for n = 1..10000</a>
%F A353731 a(n) = k if A352808(k) = prime(n). - _Michael S. Branicky_, May 17 2022
%o A353731 (Python)
%o A353731 from sympy import nextprime
%o A353731 from itertools import count, islice
%o A353731 def agen(): # generator of terms
%o A353731     A352808lst = [0, 1]; A352808set = {0, 1}
%o A353731     mink = p = 2
%o A353731     for n in count(2):
%o A353731         ahalf, k = A352808lst[n//2], mink
%o A353731         while k in A352808set or k&ahalf: k += 1
%o A353731         A352808lst.append(k); A352808set.add(k)
%o A353731         while mink in A352808set: mink += 1
%o A353731         while p in A352808set: yield A352808lst.index(p); p = nextprime(p)
%o A353731 print(list(islice(agen(), 76))) # _Michael S. Branicky_, May 17 2022
%Y A353731 Cf. A352808, A353732.
%K A353731 nonn
%O A353731 1,1
%A A353731 _N. J. A. Sloane_, May 17 2022