%I #49 Sep 08 2022 08:45:18

%S 7,17,71,1117,1171,11117,11171,1111711,1117111,1171111,11111117,

%T 11111171,71111111,1117111111,1711111111,17111111111,1111171111111,

%U 11111111111111171,11111111171111111,1111111111111111171,1111171111111111111,1111711111111111111

%N Primes with digital product = 7.

%C Subsequence of A034054. - _Michel Marcus_, Jul 27 2016

%C From _Bernard Schott_, Jul 12 2021: (Start)

%C This sequence was the subject of the 1st problem, submitted by USSR, during the 31st International Mathematical Olympiad in 1990 at Beijing, but the jury decided not to use it in the competition.

%C Problem was: Consider the m-digit numbers consisting of one '7' and m-1 '1'. For what values of m are all these numbers prime? (see the reference).

%C Answer is: only for m = 1 and m = 2, all these m-digit numbers are primes, so, a(1) = 7, then a(2) = 17 and a(3) = 71.

%C For other results, see A346274. (End)

%D Derek Holton, A Second Step to Mathematical Olympiad Problems, Vol. 7, Mathematical Olympiad Series, World Scientific, 2011, & 8.2. USS 1 p. 260 and & 8.14 Solutions pp 284-287.

%H Michael S. Branicky, <a href="/A107693/b107693.txt">Table of n, a(n) for n = 1..1318</a> (all terms with <= 1000 digits)

%H <a href="/index/O#Olympiads">Index to sequences related to Olympiads</a>.

%e 1117 and 1171 are primes, but 1711 = 29 * 59 and 7111 = 13 * 547; hence a(4) = 1117 and a(5) = 1171.

%t Flatten[ Table[ Select[ Sort[ FromDigits /@ Permutations[ Flatten[{7, Table[1, {n}]}]]], PrimeQ[ # ] &], {n, 0, 20}]]

%t Select[Prime[Range[3 10^6]], Times@@IntegerDigits[#] == 7 &] (* _Vincenzo Librandi_, Jul 27 2016 *)

%t Sort[Flatten[Table[Select[FromDigits/@Permutations[PadRight[{7},n,1]],PrimeQ],{n,20}]]] (* _Harvey P. Dale_, Aug 19 2021 *)

%o (Magma) [p: p in PrimesUpTo(3*10^8) | &*Intseq(p) eq 7]; // _Vincenzo Librandi_, Jul 27 2016

%o (Python)

%o from sympy import isprime

%o def auptod(maxdigits):

%o alst = []

%o for d in range(1, maxdigits+1):

%o if d%3 == 0: continue

%o for i in range(d):

%o t = int('1'*(d-1-i) + '7' + '1'*i)

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

%o return alst

%o print(auptod(20)) # _Michael S. Branicky_, Jul 12 2021

%Y Cf. A034054.

%Y Cf. A004022, A107612, A107689, A107690, A107691, A107692, A107694, A107695, A107696, A107697, A107698.

%Y Cf. A346274.

%K base,nonn

%O 1,1

%A _Zak Seidov_ and _Robert G. Wilson v_, May 20 2005

%E a(21) and beyond from _Michael S. Branicky_, Jul 12 2021