login
A082755
Smaller of a pair of consecutive primes having only prime digits.
4
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
Sequence in context: A082520 A062597 A038526 * A042067 A333803 A338262
KEYWORD
base,nonn
AUTHOR
Amarnath Murthy, Apr 18 2003
EXTENSIONS
Edited and extended by Robert G. Wilson v, Apr 22 2003
STATUS
approved