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A082756
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Larger of a pair of consecutive primes having only prime digits.
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2
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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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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LINKS
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Michael S. Branicky, Table of n, a(n) for n = 1..10000
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EXAMPLE
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227 is a term as the previous prime 223 also has only prime digits.
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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Cf. A019546, A082755.
Sequence in context: A088092 A174271 A211678 * A268693 A068832 A046472
Adjacent sequences: A082753 A082754 A082755 * A082757 A082758 A082759
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KEYWORD
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base,nonn
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AUTHOR
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Amarnath Murthy, Apr 18 2003
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EXTENSIONS
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Edited and extended by Robert G. Wilson v, Apr 22 2003
a(38) and beyond from Michael S. Branicky, Mar 11 2022
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STATUS
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approved
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