A373044 - OEIS

%I #40 May 21 2024 11:13:59

%S 2,3,5,7,11,23,67,89,101,4567,10111,67891,89101,789101,4567891,

%T 23456789,56789101,1234567891,45678910111,12345678910111,

%U 1112123456789101,23456789101112123,112123456789101112123,891011121234567891011,4567891011121234567891

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

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

%C a(59) has 1325 digits.

%H Michael S. Branicky, <a href="/A373044/b373044.txt">Table of n, a(n) for n = 1..58</a>

%H Eric Angelini, <a href="https://cinquantesignes.blogspot.com/2024/05/philip-gustons-primes.html">Philip Guston's primes</a>

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

%o (Python)

%o import heapq

%o from sympy import isprime

%o from itertools import islice

%o def agen(): # generator of terms

%o     digits = [1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 0, 1, 1, 1, 2]

%o     h = [(digits[i], i) for i in range(len(digits))]

%o     found = set()

%o     while True:

%o         v, last = heapq.heappop(h)

%o         if v not in found and isprime(v):

%o             found.add(v)

%o             yield v

%o         nxt = (last+1)%len(digits)

%o         heapq.heappush(h, (v*10+digits[nxt], nxt))

%o print(list(islice(agen(), 25)))

%o (PARI)

%o 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_upto_length(L)=concat([A373044_row(r)|r<-[1..L]]) \\ _M. F. Hasler_, May 21 2024

%Y Cf. A036342, A373045.

%K nonn,base

%O 1,1

%A _Eric Angelini_ and _Michael S. Branicky_, May 20 2024