|
%I #24 Jan 28 2023 10:34:52
%S 919,929,9222229,9888889,9222222222229,
%T 9888888888888888888888888888888888888888888888888888888888888888888888889
%N Primes which are a sandwich of numbers made of only one decimal digit between two 9's.
%C Conjecture: Inner digits 1, 2 and 8 are the only repeating digits for which the resulting numbers can be prime for outer digits 9. I.e., 9444..4449, 9555..5559, 9777..7779 are composite. The cases for inner digits 0, 3, 6 and 9 give composite numbers. - _Cino Hilliard_, Jul 11 2005
%C a(13) has 1141 digits. - _Michael S. Branicky_, Jan 28 2023
%H Michel Marcus, <a href="/A068689/b068689.txt">Table of n, a(n) for n = 1..12</a>
%o (PARI) lista(nn) = my(list = List(), p); for (n=1, nn, for (k=1, 8, my(d=vector(n, i, k)); d = concat(9, d); d = concat(d, 9); if (ispseudoprime(p=fromdigits(d)), listput(list, p)););); Vec(list); \\ _Michel Marcus_, Jan 28 2023
%o (Python)
%o from sympy import isprime
%o from itertools import count, islice
%o def agen(): yield from (t for i in count(1) for m in "124578" if isprime(t:=int("9" + m*i + "9")))
%o print(list(islice(agen(), 11))) # _Michael S. Branicky_, Jan 28 2023
%Y Cf. A068685, A068687, A068688.
%K nonn,base
%O 1,1
%A _Amarnath Murthy_, Mar 02 2002
%E More terms from _Sascha Kurz_, Mar 17 2002
| 