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A366596 Repdigit numbers that are divisible by 7.

%I A366596 #103 Jan 16 2024 07:00:28
%S A366596 0,7,77,777,7777,77777,111111,222222,333333,444444,555555,666666,
%T A366596 777777,888888,999999,7777777,77777777,777777777,7777777777,
%U A366596 77777777777,111111111111,222222222222,333333333333,444444444444,555555555555,666666666666,777777777777
%N A366596 Repdigit numbers that are divisible by 7.
%C A366596 7 divides a repdigit iff it consists of only digit 7, or has length 6*k (for any digit).
%C A366596 Repdigit remainders A010785(k) mod 7 have period 54. - _Karl-Heinz Hofmann_, Dec 04 2023
%H A366596 Karl-Heinz Hofmann, <a href="/A366596/b366596.txt">Table of n, a(n) for n = 1..2329</a>
%H A366596 <a href="/index/Rec#order_28">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,1000001,0,0,0,0,0,0,0,0,0,0,0,0,0,-1000000).
%F A366596 From _Karl-Heinz Hofmann_, Dec 04 2023: (Start)
%F A366596 a(n) = A010785(floor((n-2)/14)*54 + ((n-2) mod 14) + 41),   for (n-2) mod 14 >  4.
%F A366596 a(n) = (10^(6*floor((n-2)/14) + 6)-1)/9*(((n-2) mod 14)-4), for (n-2) mod 14 >  4.
%F A366596 a(n) = A010785(floor((n-2)/14)*54 + ((n-2) mod 14)*9 + 7),  for (n-2) mod 14 <= 4.
%F A366596 a(n) = (10^(6*floor((n-2)/14) + 1 + ((n-2) mod 14))-1)/9*7, for (n-2) mod 14 <= 4.
%F A366596 (End)
%o A366596 (PARI) r(n) = 10^((n+8)\9)\9*((n-1)%9+1); \\ A010785
%o A366596 lista(nn) = select(x->!(x%7), vector(nn, k, r(k-1))); \\ _Michel Marcus_, Oct 26 2023
%o A366596 (Python)
%o A366596 def A366596(n):
%o A366596     digitlen, digit = (n+12)//14*6, (n+12)%14-4
%o A366596     if digit < 1: digitlen += digit - 1; digit = 7
%o A366596     return 10**digitlen // 9 * digit # _Karl-Heinz Hofmann_, Dec 04 2023
%Y A366596 Intersection of A008589 and A010785.
%Y A366596 Cf. A002281 (a subsequence).
%Y A366596 Cf. A305322 (divisor 3), A002279 (divisor 5), A083118 (the impossible divisors).
%K A366596 nonn,base,easy
%O A366596 1,2
%A A366596 _Kritsada Moomuang_, Oct 14 2023