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A339467
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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).
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2
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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
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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
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PROG
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(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
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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STATUS
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approved
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