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%I #22 Mar 24 2024 13:02:15
%S 10,6,0,4,3,8,5,12,7,16,20,11,13,28,15,32,36,40,21,23,48,25,27,56,60,
%T 33,68,35,72,37,76,43,88,92,47,100,51,53,55,112,116,120,61,128,65,132,
%U 67,71,75,152,77,156,160,81,168,172,176,180,91,93,188,95,196,103,208,105,212
%N First appearance of prime_i in A369797 or 0 if no such appearance occurs, with p_0 being 1. (A008578 but with a different offset.)
%C As noted in A369797, a(n) is either 1 or a prime. But not mentioned is that all primes appear once, with two exceptions. The second prime, 3, never appears and the third prime, 5, appears twice, at 4 and 9.
%C A denominator of 1 in A369797 appears about 81% of the time.
%C The graph of this sequence has three broken lines, one at a(n) = 1, the second at ~3n/2 and the third at ~3n.
%t b[n_] := b[n] = (n + 2) (b[n - 1] - b[n - 2]); b[-1] = 0; b[0] = 1; a[n_] := a[n] = (3 n - 2)/GCD[3 n - 2, b[n - 2] + 2 b[n - 3]]; Flatten[ Table[ FirstPosition[ Table[ a[n], {n, 3, 220}], n], {n, Join[{1}, Prime@ Range@ 67]}]] + 2
%Y Cf. A008578, A369797.
%K nonn
%O 0,1
%A _Robert G. Wilson v_, Feb 28 2024
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