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A343834 Primes with digits in nondecreasing order, only primes, and with sum of digits also a prime.

%I A343834 #20 Jun 02 2021 02:21:26
%S A343834 2,3,5,7,23,223,227,337,557,577,2333,2357,2377,2557,2777,33377,222337,
%T A343834 222557,233357,233777,235577,2222333,2233337,2235557,3337777,3355777,
%U A343834 5555777,22222223,22233577,23333357,23377777,25577777,222222227,222222557,222222577
%N A343834 Primes with digits in nondecreasing order, only primes, and with sum of digits also a prime.
%C A343834 Intersection of A028864 and A062088.
%H A343834 Michael S. Branicky, <a href="/A343834/b343834.txt">Table of n, a(n) for n = 1..10000</a>
%t A343834 a[p_] := With[{dg = IntegerDigits@p}, PrimeQ@p && OrderedQ@dg && AllTrue[dg, PrimeQ] && PrimeQ@ Total@dg]; Cases[ Range[3*10^7], _?(a@# &)] (* or *)
%t A343834 upToDigitLen[k_] := Cases[ FromDigits@# & /@ Select[ Flatten[ Table[ Tuples[{2, 3, 5, 7}, {i}], {i, k}], 1], OrderedQ[#] &], _?(PrimeQ@# && PrimeQ@ Total@ IntegerDigits@# &)]; upToDigitLen[10]
%o A343834 (Python)
%o A343834 from sympy import isprime
%o A343834 from sympy.utilities.iterables import multiset_combinations
%o A343834 def aupton(terms):
%o A343834   n, digits, alst = 0, 1, []
%o A343834   while len(alst) < terms:
%o A343834     mcstr = "".join(d*digits for d in "2357")
%o A343834     for mc in multiset_combinations(mcstr, digits):
%o A343834       sd = sum(int(d) for d in mc)
%o A343834       if not isprime(sd): continue
%o A343834       t = int("".join(mc))
%o A343834       if isprime(t): alst.append(t)
%o A343834       if len(alst) == terms: break
%o A343834     else: digits += 1
%o A343834   return alst
%o A343834 print(aupton(35)) # _Michael S. Branicky_, May 01 2021
%Y A343834 Cf. A019546, A028864, A046704, A062088.
%K A343834 nonn,base,easy
%O A343834 1,1
%A A343834 _Mikk Heidemaa_, May 01 2021
%E A343834 a(33) and beyond from _Michael S. Branicky_, May 01 2021