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A339467 The Ronnie O'Sullivan's "infinite plant" sequence: nonprime numbers become prime numbers by striking the cue ball 1 with a cue stick to the right (see the Comments section).

%I A339467 #27 Dec 14 2020 05:16:08
%S A339467 1,12,4,14,15,6,16,18,32,8,33,9,72,34,35,36,74,38,39,75,91,76,77,92,
%T A339467 93,78,94,192,95,96,132,98,99,111,133,112,114,194,195,212,115,213,116,
%U A339467 134,196,135,214,198,117,272,118,119,291,136,138,215,216,171,273,172,231,274,217,275,218,219,292,232,234,312,235
%N A339467 The Ronnie O'Sullivan's "infinite plant" sequence: nonprime numbers become prime numbers by striking the cue ball 1 with a cue stick to the right (see the Comments section).
%C A339467 There is a non-snooker description of this sequence: first erase all spaces between terms; then move every comma 1 position to the left; the new sequence is now made by primes only (with duplicates, sometimes); the starting sequence (this one) is the lexicographically earliest with this property that has no duplicates and no primes.
%H A339467 Carole Dubois, <a href="/A339467/b339467.txt">Table of n, a(n) for n = 1..5000</a>
%e A339467 Striking 1 to the right pushes 1 against 12;
%e A339467 the last digit of 12 is then pushed against 4 (leaving 11 behind - a prime);
%e A339467 the last digit of 4 is then pushed against 14 (leaving 2 behind - a prime);
%e A339467 the last digit of 14 is then pushed against 15 (leaving 41 behind - a prime);
%e A339467 the last digit of 15 is then pushed against 6 (leaving 41 behind - a prime);
%e A339467 the last digit of 6 is then pushed against 16 (leaving 5 behind - a prime); etc.
%e A339467 This is the lexicographically earliest sequence of distinct positive terms with this property
%o A339467 (Python)
%o A339467 from sympy import isprime
%o A339467 def aupto(n):
%o A339467     alst, used = [0, 1], {1}
%o A339467     for k in range(2, n+1):
%o A339467         ball = (str(alst[k-1]))[-1]
%o A339467         ak = 1
%o A339467         ball_left = ball + (str(ak))[:-1]
%o A339467         while not isprime(int(ball_left)) or ak in used or isprime(ak):
%o A339467             ak += 1 + (ak%10 == 9)  # can't end in 0
%o A339467             ball_left = ball + (str(ak))[:-1]
%o A339467         alst.append(ak)
%o A339467         used.add(ak)
%o A339467     return alst[1:]  # use alst[n] for a(n) function
%o A339467 print(aupto(64))  # _Michael S. Branicky_, Dec 07 2020
%Y A339467 Cf. A339616 (the Judd Trump sequence), A335972, A335973.
%K A339467 base,nonn
%O A339467 1,2
%A A339467 _Eric Angelini_ and _Carole Dubois_, Dec 06 2020