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

1,1

Comments

This is a variant of A343471.

Links

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

Chris K. Caldwell and G. L. Honaker, Jr., Prime Curios! 277535577223.

Example

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.

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, 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

Crossrefs

Cf. A082755, A343471.

Subsequence of A019546.

Sequence in context: A202655 A009488 A302059 * A138247 A322709 A015506

Adjacent sequences: A352309 A352310 A352311 * A352313 A352314 A352315

Keyword

nonn,base,more

Author

Bernard Schott, Mar 11 2022

Extensions

a(9) from Michael S. Branicky, Mar 15 2022

Status

approved