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A352312 Start of the first run of exactly n consecutive primes using only prime digits. 1
7, 223, 37253, 2, 2575723, 7533777323, 277535577223, 5323733533375237, 57552737757357223 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 10 03:38 EDT 2022. Contains 356029 sequences. (Running on oeis4.)