This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A370388 #25 May 03 2025 17:56:41
%S A370388 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 A370388 33,68,35,72,37,76,43,88,92,47,100,51,53,55,112,116,120,61,128,65,132,
%U A370388 67,71,75,152,77,156,160,81,168,172,176,180,91,93,188,95,196,103,208,105,212
%N 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.)
%C A370388 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 A370388 A denominator of 1 in A369797 appears about 81% of the time.
%C A370388 The graph of this sequence has three broken lines, one at a(n) = 1, the second at ~3n/2 and the third at ~3n.
%F A370388 Conjectures from _Ridouane Oudra_, Apr 26 2025: (Start)
%F A370388 a(n) = (2/3) mod prime(n), for n>2.
%F A370388 a(n) = (prime(n)*A039701(n) + 2)/3, for n>2.
%F A370388 a(n) = A008864(n) - A283419(n), for n>2. (End)
%t A370388 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 A370388 Cf. A008578, A369797, A039701, A008864, A283419.
%K A370388 nonn
%O A370388 0,1
%A A370388 _Robert G. Wilson v_, Feb 28 2024