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Primes that contain only the digits (1, 5, 7).
3

%I #21 Dec 09 2024 14:29:24

%S 5,7,11,17,71,151,157,557,571,577,751,757,1117,1151,1171,1511,1571,

%T 1777,5171,5557,5711,5717,7151,7177,7517,7577,7717,7757,11117,11171,

%U 11177,11551,11717,11777,15511,15551,17117,17551,51151,51157,51511,51517,51551,51577

%N Primes that contain only the digits (1, 5, 7).

%H Alois P. Heinz, <a href="/A260828/b260828.txt">Table of n, a(n) for n = 1..10000</a>

%H James Maynard and Brady Haran, <a href="https://www.youtube.com/watch?v=eeoBCS7IEqs">Primes without a 7</a>, Numberphile video (2019)

%t Select[Prime[Range[2 10^4]], Complement[IntegerDigits[#], {1, 5, 7}] == {} &]

%o (Magma) [p: p in PrimesUpTo(2*10^5) | Set(Intseq(p)) subset [1,5,7]];

%o (Python)

%o from sympy import isprime

%o from sympy.utilities.iterables import multiset_permutations

%o def aupton(terms):

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

%o while len(alst) < terms:

%o mpstr = "".join(d*digits for d in "157")

%o for mp in multiset_permutations(mpstr, digits):

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

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

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

%o else: digits += 1

%o return alst

%o print(aupton(44)) # _Michael S. Branicky_, May 07 2021

%Y Subsequence of A030096. A020453, A020455 and A020467 are subsequences.

%Y Cf. similar sequences listed in A260827.

%Y Cf. A000040.

%K nonn,easy,base

%O 1,1

%A _Vincenzo Librandi_, Aug 02 2015