A082755 Smaller of a pair of consecutive primes having only prime digits.

2, 3, 5, 223, 727, 3253, 3727, 5233, 5323, 7573, 7723, 7753, 22273, 23327, 25523, 27733, 32233, 32323, 32533, 35323, 35533, 37253, 37273, 52223, 52727, 53323, 53327, 53773, 55333, 72223, 72727, 75223, 75527, 75553, 222527, 222533, 222553, 223273, 223753, 225223

Offset

1,1

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000 (Terms for n = 1..1000 from Harvey P. Dale)

Example

223 is a term as the next prime 227 also has only prime digits.

Mathematica

NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; p = 0; q = 1; pd = {1}; Do[p = q; pd = qd; q = NextPrim[p]; qd = Union[ Join[{2, 3, 5, 7}, IntegerDigits[q]]]; If[pd == qd == {2, 3, 5, 7}, Print[p]], {n, 1, 20000}]
Prime[#]&/@SequencePosition[Table[If[AllTrue[IntegerDigits[n], PrimeQ], 1, 0], {n, Prime[Range[20000]]}], {1, 1}][[All, 1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 31 2017 *)

Prog

(Python)
from sympy import nextprime, isprime
from itertools import count, islice, product
def onlypd(n): return set(str(n)) <= set("2357")
def agen():
    yield from [2, 3, 5]
    for digits in count(2):
        for p in product("2357", repeat=digits-1):
            for end in "37":
                t = int("".join(p) + end)
                if isprime(t) and onlypd(nextprime(t)):
                    yield t
print(list(islice(agen(), 40))) # Michael S. Branicky, Mar 11 2022

Crossrefs

Cf. A019546, A082756.

Sequence in context: A082520 A062597 A038526 * A042067 A333803 A338262

Adjacent sequences: A082752 A082753 A082754 * A082756 A082757 A082758

Keyword

base,nonn

Author

Amarnath Murthy, Apr 18 2003

Extensions

Edited and extended by Robert G. Wilson v, Apr 22 2003

Status

approved