A036342 Prime concatenated analog clock numbers read clockwise.

2, 3, 5, 7, 11, 23, 67, 89, 4567, 23456789, 23456789101112123, 891011121234567891011, 23456789101112123456789101112123, 567891011121234567891011121234567891011, 121234567891011121234567891011121234567891011121, 91011121234567891011121234567891011121234567891011121234567

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(28) has 1325 digits. - Michael S. Branicky, May 20 2024

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..27 (terms 1..25 from Sean A. Irvine)
• Carlos Rivera, Puzzle 19. Primes on a clock, The Prime Puzzles & Problems Connection.
• Eric Weisstein's World of Mathematics, Clock Prime.

Crossrefs

Cf. A034326, A036343, A036344.

Programs

Python

import heapq
from sympy import isprime
from itertools import islice
def A036342_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 = 1 if last == 12 else last+1
        shift = 10 if nxt < 10 else 100
        heapq.heappush(h, (v*shift+nxt, nxt))
print(list(islice(A036342_gen(), 16))) # Michael S. Branicky, May 20 2024

Extensions

a(14)-a(15) from Jean-Marie Hachey, Oct 05 2016

Offset and data corrected by Sean A. Irvine, Oct 26 2020