A339616 The Judd Trump's "infinite plant" sequence: prime numbers become nonprime numbers by striking the cue ball 2 with a cue stick to the right (see the Comments section).

2, 11, 3, 23, 29, 5, 13, 31, 7, 41, 43, 37, 47, 53, 59, 17, 61, 67, 71, 83, 89, 19, 97, 73, 101, 103, 107, 79, 109, 127, 113, 149, 131, 151, 157, 137, 139, 163, 167, 173, 181, 179, 211, 191, 193, 197, 223, 199, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 281, 283, 277, 293, 307, 311, 331, 337, 313, 347

Offset: 1

Author

Eric Angelini and Carole Dubois, Dec 10 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 nonprimes only (with duplicates, sometimes); the starting sequence (this one) is the lexicographically earliest with this property that has no duplicates and no nonprimes.

Examples

			Striking 2 to the right pushes 2 against 11;
the last digit of 11 is then pushed against 3 (leaving 21 behind - a nonprime);
the last digit of 3 is then pushed against 23 (leaving 1 behind - a nonprime);
the last digit of 23 is then pushed against 29 (leaving 32 behind - a nonprime);
the last digit of 29 is then pushed against 5 (leaving 32 behind - a nonprime);
the last digit of 5 is then pushed against 13 (leaving 9 behind - a nonprime);
etc.
This is the lexicographically earliest sequence of distinct positive terms with this property.
		

Crossrefs

Cf. A339467 (the Ronnie O'Sullivan sequence).

Programs

Python

from sympy import isprime
def aupto(n):
    alst, used, strakm1 = [0, 2], {2}, "2"
    for k in range(2, n+1):
        ball = (str(alst[k-1]))[-1]
        ak = 1
        ball_left = ball + (str(ak))[:-1]
        while isprime(int(ball_left)) or ak in used or not isprime(ak):
            ak += 2 # continue to only test odds
            ball_left = ball + (str(ak))[:-1]
        alst.append(ak)
        used.add(ak)
    return alst[1:]  # use alst[n] for a(n) function
print(aupto(70)) # Michael S. Branicky, Dec 11 2020