A373044 Prime concatenated analog clock numbers read clockwise. Version 2: hours > 9 are split in 2 digits.

2, 3, 5, 7, 11, 23, 67, 89, 101, 4567, 10111, 67891, 89101, 789101, 4567891, 23456789, 56789101, 1234567891, 45678910111, 12345678910111, 1112123456789101, 23456789101112123, 112123456789101112123, 891011121234567891011, 4567891011121234567891

Offset

1,1

Comments

In this version, the numbers 10, 11, and 12 may be split up into individual digits, in contrast to A036342.

a(59) has 1325 digits.

Links

Michael S. Branicky, Table of n, a(n) for n = 1..58

Eric Angelini, Philip Guston's primes

Tiziano Mosconi, in reply to Carlos Rivera, Puzzle 19: Primes on a clock, primepuzzles.net, Aug 13 2001.

Example

101 is a term here using the digits 1 and 0 from 10 and the first 1 of 11.

Prog

(Python)
import heapq
from sympy import isprime
from itertools import islice
def agen(): # generator of terms
    digits = [1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 0, 1, 1, 1, 2]
    h = [(digits[i], i) for i in range(len(digits))]
    found = set()
    while True:
        v, last = heapq.heappop(h)
        if v not in found and isprime(v):
            found.add(v)
            yield v
        nxt = (last+1)%len(digits)
        heapq.heappush(h, (v*10+digits[nxt], nxt))
print(list(islice(agen(), 25)))
(PARI)
A373044_row(r)={my(d=concat([digits(i)|i<-[1..12]]), p); Set([p| s<-[1..#d], d[s]&& isprime(p=fromdigits([d[i%#d+1]| i<-[s-1..s+r-2]]))])}\\ r-digit-terms
A373044_upto_length(L)=concat([A373044_row(r)|r<-[1..L]]) \\ M. F. Hasler, May 21 2024

Crossrefs

Cf. A036342, A373045.

Sequence in context: A119660 A079148 A107367 * A036342 A114421 A167119

Adjacent sequences: A373041 A373042 A373043 * A373045 A373046 A373047

Keyword

nonn,base

Author

Eric Angelini and Michael S. Branicky, May 20 2024

Status

approved