OFFSET
1,1
COMMENTS
Subsequence of A034054. - Michel Marcus, Jul 27 2016
From Bernard Schott, Jul 12 2021: (Start)
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.
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).
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.
For other results, see A346274. (End)
REFERENCES
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.
LINKS
Michael S. Branicky, Table of n, a(n) for n = 1..1318 (all terms with <= 1000 digits)
EXAMPLE
1117 and 1171 are primes, but 1711 = 29 * 59 and 7111 = 13 * 547; hence a(4) = 1117 and a(5) = 1171.
MATHEMATICA
Flatten[ Table[ Select[ Sort[ FromDigits /@ Permutations[ Flatten[{7, Table[1, {n}]}]]], PrimeQ[ # ] &], {n, 0, 20}]]
Select[Prime[Range[3 10^6]], Times@@IntegerDigits[#] == 7 &] (* Vincenzo Librandi, Jul 27 2016 *)
Sort[Flatten[Table[Select[FromDigits/@Permutations[PadRight[{7}, n, 1]], PrimeQ], {n, 20}]]] (* Harvey P. Dale, Aug 19 2021 *)
PROG
(Magma) [p: p in PrimesUpTo(3*10^8) | &*Intseq(p) eq 7]; // Vincenzo Librandi, Jul 27 2016
(Python)
from sympy import isprime
def auptod(maxdigits):
alst = []
for d in range(1, maxdigits+1):
if d%3 == 0: continue
for i in range(d):
t = int('1'*(d-1-i) + '7' + '1'*i)
if isprime(t): alst.append(t)
return alst
print(auptod(20)) # Michael S. Branicky, Jul 12 2021
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Zak Seidov and Robert G. Wilson v, May 20 2005
EXTENSIONS
a(21) and beyond from Michael S. Branicky, Jul 12 2021
STATUS
approved