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A366596
Repdigit numbers that are divisible by 7.
3
0, 7, 77, 777, 7777, 77777, 111111, 222222, 333333, 444444, 555555, 666666, 777777, 888888, 999999, 7777777, 77777777, 777777777, 7777777777, 77777777777, 111111111111, 222222222222, 333333333333, 444444444444, 555555555555, 666666666666, 777777777777
OFFSET
1,2
COMMENTS
7 divides a repdigit iff it consists of only digit 7, or has length 6*k (for any digit).
Repdigit remainders A010785(k) mod 7 have period 54. - Karl-Heinz Hofmann, Dec 04 2023
LINKS
Index entries for linear recurrences with constant coefficients, 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).
FORMULA
From Karl-Heinz Hofmann, Dec 04 2023: (Start)
a(n) = A010785(floor((n-2)/14)*54 + ((n-2) mod 14) + 41), for (n-2) mod 14 > 4.
a(n) = (10^(6*floor((n-2)/14) + 6)-1)/9*(((n-2) mod 14)-4), for (n-2) mod 14 > 4.
a(n) = A010785(floor((n-2)/14)*54 + ((n-2) mod 14)*9 + 7), for (n-2) mod 14 <= 4.
a(n) = (10^(6*floor((n-2)/14) + 1 + ((n-2) mod 14))-1)/9*7, for (n-2) mod 14 <= 4.
(End)
PROG
(PARI) r(n) = 10^((n+8)\9)\9*((n-1)%9+1); \\ A010785
lista(nn) = select(x->!(x%7), vector(nn, k, r(k-1))); \\ Michel Marcus, Oct 26 2023
(Python)
def A366596(n):
digitlen, digit = (n+12)//14*6, (n+12)%14-4
if digit < 1: digitlen += digit - 1; digit = 7
return 10**digitlen // 9 * digit # Karl-Heinz Hofmann, Dec 04 2023
CROSSREFS
Intersection of A008589 and A010785.
Cf. A002281 (a subsequence).
Cf. A305322 (divisor 3), A002279 (divisor 5), A083118 (the impossible divisors).
Sequence in context: A191465 A229281 A144071 * A061546 A002281 A097983
KEYWORD
nonn,base,easy
AUTHOR
Kritsada Moomuang, Oct 14 2023
STATUS
approved