A036343 Prime concatenated analog clock numbers read counterclockwise.

2, 3, 5, 7, 11, 43, 109, 10987, 76543, 6543211211, 4321121110987, 3211211109876543211211, 43211211109876543211211109876543, 9876543211211109876543211211109876543211211109876543211211

Offset: 1

Author

Patrick De Geest, Dec 15 1998

Keywords

• nonn
• base

Comments

The hours 10, 11 and 12 are taken 'complete and unreversed'.

a(19) has 1139 digits. - Michael S. Branicky, May 20 2024

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..18
• Carlos Rivera, Puzzle 19. Primes on a clock, The Prime Puzzles & Problems Connection.
• Eric Weisstein's World of Mathematics, Clock Prime.

Crossrefs

Cf. A034326, A036342, A036344.

Programs

Python

import heapq
from sympy import isprime
from itertools import islice
def A036343_gen(): # generator of terms
    h = [(i, i) for i in range(1, 13)]
    while True:
        v, last = heapq.heappop(h)
        if isprime(v):
            yield v
        nxt = 12 if last == 1 else last-1
        shift = 10 if nxt < 10 else 100
        heapq.heappush(h, (v*shift+nxt, nxt))
print(list(islice(A036343_gen(), 16))) # Michael S. Branicky, May 20 2024

Extensions

Offset corrected by Sean A. Irvine, Oct 26 2020