|
|
A343834
|
|
Primes with digits in nondecreasing order, only primes, and with sum of digits also a prime.
|
|
1
|
|
|
2, 3, 5, 7, 23, 223, 227, 337, 557, 577, 2333, 2357, 2377, 2557, 2777, 33377, 222337, 222557, 233357, 233777, 235577, 2222333, 2233337, 2235557, 3337777, 3355777, 5555777, 22222223, 22233577, 23333357, 23377777, 25577777, 222222227, 222222557, 222222577
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
|
|
LINKS
|
|
|
MATHEMATICA
|
a[p_] := With[{dg = IntegerDigits@p}, PrimeQ@p && OrderedQ@dg && AllTrue[dg, PrimeQ] && PrimeQ@ Total@dg]; Cases[ Range[3*10^7], _?(a@# &)] (* or *)
upToDigitLen[k_] := Cases[ FromDigits@# & /@ Select[ Flatten[ Table[ Tuples[{2, 3, 5, 7}, {i}], {i, k}], 1], OrderedQ[#] &], _?(PrimeQ@# && PrimeQ@ Total@ IntegerDigits@# &)]; upToDigitLen[10]
|
|
PROG
|
(Python)
from sympy import isprime
from sympy.utilities.iterables import multiset_combinations
def aupton(terms):
n, digits, alst = 0, 1, []
while len(alst) < terms:
mcstr = "".join(d*digits for d in "2357")
for mc in multiset_combinations(mcstr, digits):
sd = sum(int(d) for d in mc)
if not isprime(sd): continue
t = int("".join(mc))
if isprime(t): alst.append(t)
if len(alst) == terms: break
else: digits += 1
return alst
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,base,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|