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 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 Intersection of A028864 and A062088. LINKS Michael S. Branicky, Table of n, a(n) for n = 1..10000 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 print(aupton(35)) # Michael S. Branicky, May 01 2021 CROSSREFS Cf. A019546, A028864, A046704, A062088. Sequence in context: A277575 A289754 A062088 * A070029 A360497 A368805 Adjacent sequences: A343831 A343832 A343833 * A343835 A343836 A343837 KEYWORD nonn,base,easy AUTHOR Mikk Heidemaa, May 01 2021 EXTENSIONS a(33) and beyond from Michael S. Branicky, May 01 2021 STATUS approved

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Last modified June 24 00:02 EDT 2024. Contains 373661 sequences. (Running on oeis4.)