A373045 Prime concatenated analog clock numbers read counterclockwise. Version 2: hours > 9 may be split into individual digits.
2, 3, 5, 7, 11, 19, 43, 101, 211, 1019, 1987, 2111, 21211, 76543, 101987, 432121, 4321211, 12111019, 6543212111, 9876543212111, 1019876543212111019, 654321211101987654321211, 4321211101987654321211101, 6543212111019876543212111, 76543212111019876543212111019
Offset: 1
Links
- Michael S. Branicky, Table of n, a(n) for n = 1..46
- 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
A373045_row(r)={my(d=concat([digits(i)|i<-[1..12]]), p); Set([p| s<-[1..#d], d[s]&& isprime(p=fromdigits([d[(s-i)%#d+1]| i<-[1..r]]))])}\\ r-digit-terms A373045_upto_length(L)=concat([A373045_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))) # Michael S. Branicky, May 20 2024
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