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Primes with digits in nondecreasing order, only primes, and with sum of digits also a prime.
1

%I #20 Jun 02 2021 02:21:26

%S 2,3,5,7,23,223,227,337,557,577,2333,2357,2377,2557,2777,33377,222337,

%T 222557,233357,233777,235577,2222333,2233337,2235557,3337777,3355777,

%U 5555777,22222223,22233577,23333357,23377777,25577777,222222227,222222557,222222577

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

%C Intersection of A028864 and A062088.

%H Michael S. Branicky, <a href="/A343834/b343834.txt">Table of n, a(n) for n = 1..10000</a>

%t a[p_] := With[{dg = IntegerDigits@p}, PrimeQ@p && OrderedQ@dg && AllTrue[dg, PrimeQ] && PrimeQ@ Total@dg]; Cases[ Range[3*10^7], _?(a@# &)] (* or *)

%t upToDigitLen[k_] := Cases[ FromDigits@# & /@ Select[ Flatten[ Table[ Tuples[{2, 3, 5, 7}, {i}], {i, k}], 1], OrderedQ[#] &], _?(PrimeQ@# && PrimeQ@ Total@ IntegerDigits@# &)]; upToDigitLen[10]

%o (Python)

%o from sympy import isprime

%o from sympy.utilities.iterables import multiset_combinations

%o def aupton(terms):

%o n, digits, alst = 0, 1, []

%o while len(alst) < terms:

%o mcstr = "".join(d*digits for d in "2357")

%o for mc in multiset_combinations(mcstr, digits):

%o sd = sum(int(d) for d in mc)

%o if not isprime(sd): continue

%o t = int("".join(mc))

%o if isprime(t): alst.append(t)

%o if len(alst) == terms: break

%o else: digits += 1

%o return alst

%o print(aupton(35)) # _Michael S. Branicky_, May 01 2021

%Y Cf. A019546, A028864, A046704, A062088.

%K nonn,base,easy

%O 1,1

%A _Mikk Heidemaa_, May 01 2021

%E a(33) and beyond from _Michael S. Branicky_, May 01 2021