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.)

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.

Links

Table of n, a(n) for n=0..66.

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

Cf. A008578, A369797.

Sequence in context: A276348 A281400 A283726 * A010171 A006518 A094175

Adjacent sequences: A370385 A370386 A370387 * A370389 A370390 A370391

Keyword

nonn

Author

Robert G. Wilson v, Feb 28 2024

Status

approved