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

%I A373044 #40 May 21 2024 11:13:59
%S A373044 2,3,5,7,11,23,67,89,101,4567,10111,67891,89101,789101,4567891,
%T A373044 23456789,56789101,1234567891,45678910111,12345678910111,
%U A373044 1112123456789101,23456789101112123,112123456789101112123,891011121234567891011,4567891011121234567891
%N A373044 Prime concatenated analog clock numbers read clockwise.  Version 2: hours > 9 are split in 2 digits.
%C A373044 In this version, the numbers 10, 11, and 12 may be split up into individual digits, in contrast to A036342.
%C A373044 a(59) has 1325 digits.
%H A373044 Michael S. Branicky, <a href="/A373044/b373044.txt">Table of n, a(n) for n = 1..58</a>
%H A373044 Eric Angelini, <a href="https://cinquantesignes.blogspot.com/2024/05/philip-gustons-primes.html">Philip Guston's primes</a>
%H A373044 Tiziano Mosconi, in reply to Carlos Rivera, <a href="https://www.primepuzzles.net/puzzles/puzz_019.htm">Puzzle 19: Primes on a clock</a>, primepuzzles.net, Aug 13 2001.
%e A373044 101 is a term here using the digits 1 and 0 from 10 and the first 1 of 11.
%o A373044 (Python)
%o A373044 import heapq
%o A373044 from sympy import isprime
%o A373044 from itertools import islice
%o A373044 def agen(): # generator of terms
%o A373044     digits = [1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 0, 1, 1, 1, 2]
%o A373044     h = [(digits[i], i) for i in range(len(digits))]
%o A373044     found = set()
%o A373044     while True:
%o A373044         v, last = heapq.heappop(h)
%o A373044         if v not in found and isprime(v):
%o A373044             found.add(v)
%o A373044             yield v
%o A373044         nxt = (last+1)%len(digits)
%o A373044         heapq.heappush(h, (v*10+digits[nxt], nxt))
%o A373044 print(list(islice(agen(), 25)))
%o A373044 (PARI)
%o A373044 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
%o A373044 A373044_upto_length(L)=concat([A373044_row(r)|r<-[1..L]]) \\ _M. F. Hasler_, May 21 2024
%Y A373044 Cf. A036342, A373045.
%K A373044 nonn,base
%O A373044 1,1
%A A373044 _Eric Angelini_ and _Michael S. Branicky_, May 20 2024