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