A343471 Start of the first run of n or more consecutive primes using only prime digits.
2, 2, 2, 2, 2575723, 7533777323, 277535577223, 5323733533375237, 57552737757357223
Offset: 1
Examples
a(1) = 2 because it is the first prime using only prime digits. a(2) = 2 because 2, 3 is the first pair of consecutive primes using only prime digits. a(5) = 2575723 because 2575723, 2575733, 2575753, 2575757, 2575777 is the first run of 5 consecutive primes using only prime digits.
Links
- Chris K. Caldwell and G. L. Honaker, Jr., Prime Curios! 277535577223
Programs
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Python
from sympy import nextprime, isprime from itertools import count, islice, product def onlypd(n): return set(str(n)) <= set("2357") def agen(): adict = {i:2 for i in range(1, 5)} for i in range(1, 5): yield 2 for digits in count(2): for p in product("2357", repeat=digits-1): for end in "37": t0 = t = int("".join(p) + end) run = 0 while isprime(t): run += 1 t = nextprime(t) if not onlypd(t): break if run not in adict: for r in range(max(adict)+1, run+1): adict[r] = t0 yield t0 print(list(islice(agen(), 6))) # Michael S. Branicky, Mar 11 2022
Extensions
a(8) from Daniel Suteu, Apr 22 2021
a(9) from Michael S. Branicky, Mar 15 2022
Comments