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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). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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.

LINKS

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

EXAMPLE

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

PROG

(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

CROSSREFS

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

Sequence in context: A328285 A307164 A181829 * A199693 A166206 A040137

Adjacent sequences:  A339464 A339465 A339466 * A339468 A339469 A339470

KEYWORD

base,nonn

AUTHOR

Eric Angelini and Carole Dubois, Dec 06 2020

STATUS

approved

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Last modified January 25 10:12 EST 2022. Contains 350565 sequences. (Running on oeis4.)