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A343471
Start of the first run of n or more consecutive primes using only prime digits.
1
2, 2, 2, 2, 2575723, 7533777323, 277535577223, 5323733533375237, 57552737757357223
OFFSET
1,1
COMMENTS
This is a variant of A352312. - Bernard Schott, Mar 24 2022
LINKS
Chris K. Caldwell and G. L. Honaker, Jr., Prime Curios! 277535577223
EXAMPLE
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.
PROG
(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
CROSSREFS
KEYWORD
nonn,base,hard,more
AUTHOR
Metin Sariyar, Apr 16 2021
EXTENSIONS
a(8) from Daniel Suteu, Apr 22 2021
a(9) from Michael S. Branicky, Mar 15 2022
STATUS
approved