A352312 Start of the first run of exactly n consecutive primes using only prime digits.
7, 223, 37253, 2, 2575723, 7533777323, 277535577223, 5323733533375237, 57552737757357223
Offset: 1
Examples
a(1) = 7 because it is the first prime using only prime digits and whose next prime 11 does not use only prime digits. a(3) = 37253 because 37253, 37273, 37277 is the first run of 3 consecutive primes using only prime digits, then next prime 37307 has a digit 0.
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, n = {1:7, 4:2}, 1 yield 7 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: adict[run] = t0 if run > n: for r in range(n+1, run+1): if r in adict: yield adict[r] n += 1 print(list(islice(agen(), 6))) # Michael S. Branicky, Mar 11 2022
Extensions
a(9) from Michael S. Branicky, Mar 15 2022
Comments