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

Author

Metin Sariyar, Apr 16 2021

Keywords

• nonn
• base
• hard
• more

Comments

This is a variant of A352312. - Bernard Schott, Mar 24 2022

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

Crossrefs

Cf. A019546, A082755, A352312.

Programs

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