A082756 Larger of a pair of consecutive primes having only prime digits.

3, 5, 7, 227, 733, 3257, 3733, 5237, 5333, 7577, 7727, 7757, 22277, 23333, 25537, 27737, 32237, 32327, 32537, 35327, 35537, 37273, 37277, 52237, 52733, 53327, 53353, 53777, 55337, 72227, 72733, 75227, 75533, 75557, 222533, 222553, 222557, 223277, 223757, 225227

Offset

1,1

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Example

227 is a term as the previous prime 223 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[q]], {n, 1, 20000}]
Transpose[Select[Partition[Prime[Range[20000]], 2, 1], And@@PrimeQ[ Flatten[ IntegerDigits/@#]]&]] [[2]] (* Harvey P. Dale, Jul 19 2011 *)

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 [3, 5, 7]
    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):
                    t2 = nextprime(t)
                    if onlypd(t2):
                        yield t2
print(list(islice(agen(), 40))) # Michael S. Branicky, Mar 11 2022

Crossrefs

Cf. A019546, A082755.

Sequence in context: A088092 A174271 A211678 * A268693 A068832 A046472

Adjacent sequences: A082753 A082754 A082755 * A082757 A082758 A082759

Keyword

base,nonn

Author

Amarnath Murthy, Apr 18 2003

Extensions

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

a(38) and beyond from Michael S. Branicky, Mar 11 2022

Status

approved