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A370388
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.)
0
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, 33, 68, 35, 72, 37, 76, 43, 88, 92, 47, 100, 51, 53, 55, 112, 116, 120, 61, 128, 65, 132, 67, 71, 75, 152, 77, 156, 160, 81, 168, 172, 176, 180, 91, 93, 188, 95, 196, 103, 208, 105, 212
OFFSET
0,1
COMMENTS
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.
A denominator of 1 in A369797 appears about 81% of the time.
The graph of this sequence has three broken lines, one at a(n) = 1, the second at ~3n/2 and the third at ~3n.
MATHEMATICA
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
CROSSREFS
Sequence in context: A276348 A281400 A283726 * A010171 A006518 A094175
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Feb 28 2024
STATUS
approved