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).

1, 12, 4, 14, 15, 6, 16, 18, 32, 8, 33, 9, 72, 34, 35, 36, 74, 38, 39, 75, 91, 76, 77, 92, 93, 78, 94, 192, 95, 96, 132, 98, 99, 111, 133, 112, 114, 194, 195, 212, 115, 213, 116, 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

Offset: 1

Author

Eric Angelini and Carole Dubois, Dec 06 2020

Keywords

• base
• nonn

Comments

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.

Examples

			Striking 1 to the right pushes 1 against 12;
the last digit of 12 is then pushed against 4 (leaving 11 behind - a prime);
the last digit of 4 is then pushed against 14 (leaving 2 behind - a prime);
the last digit of 14 is then pushed against 15 (leaving 41 behind - a prime);
the last digit of 15 is then pushed against 6 (leaving 41 behind - a prime);
the last digit of 6 is then pushed against 16 (leaving 5 behind - a prime); etc.
This is the lexicographically earliest sequence of distinct positive terms with this property
		

Links

• Carole Dubois, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A339616 (the Judd Trump sequence), A335972, A335973.

Programs

Python

from sympy import isprime
def aupto(n):
    alst, used = [0, 1], {1}
    for k in range(2, n+1):
        ball = (str(alst[k-1]))[-1]
        ak = 1
        ball_left = ball + (str(ak))[:-1]
        while not isprime(int(ball_left)) or ak in used or isprime(ak):
            ak += 1 + (ak%10 == 9)  # can't end in 0
            ball_left = ball + (str(ak))[:-1]
        alst.append(ak)
        used.add(ak)
    return alst[1:]  # use alst[n] for a(n) function
print(aupto(64))  # Michael S. Branicky, Dec 07 2020