A339467 -id:A339467 - cp's OEIS frontend

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

Eric Angelini and Carole Dubois, Dec 10 2020

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.

			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.

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

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

A381224 a(n) is the integer resulting from the concatenation of the unit digit of prime(n-1) to the digits of prime(n) without its own unit digit.

Original entry on oeis.org

0, 2, 3, 5, 71, 11, 31, 71, 92, 32, 93, 13, 74, 14, 34, 75, 35, 96, 16, 77, 17, 37, 98, 38, 99, 710, 110, 310, 710, 911, 312, 713, 113, 713, 914, 915, 115, 716, 316, 717, 317, 918, 119, 119, 319, 719, 921, 122, 322, 722, 923, 323, 924, 125, 125, 726, 326, 927, 127, 728, 128, 329, 330, 731, 131, 331, 733, 133, 734, 734, 935, 335

Offset: 1

N. J. A. Sloane, Feb 22 2025

Take list of primes and move the right-most digit of each term to the start of the next term.

Inspired by Eric Angelini and Carole Dubois's A339467.

			Starting from
   2, 3, 5, 7, 11, 13, 17, 19, ...
we get
   0, 2, 3, 5, 71, 11, 31, 71, ...

N. J. A. Sloane, Table of n, a(n) for n = 1..10000

Cf. A000040, A032759, A290148, A339467.

a381224 := proc(n) local i,p;
if n=1 then i:=0; else i:=(ithprime(n-1) mod 10); fi;
p:=ithprime(n);
i * 10^ilog10(p) + floor(p/10);
end;

from sympy import prime
def a(n): return 0 if n == 1 else int(str(prime(n-1)%10)+ str(prime(n))[:-1])
print([a(n) for n in range(1, 73)]) # Michael S. Branicky, Feb 22 2025

cp's OEIS Frontend

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).

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