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

1,1

Comments

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

Links

Table of n, a(n) for n=1..9.

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

Cf. A019546, A082755, A352312.

Sequence in context: A084957 A239944 A235812 * A035307 A292373 A305383

Adjacent sequences: A343468 A343469 A343470 * A343472 A343473 A343474

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