A366596 Repdigit numbers that are divisible by 7.

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

Karl-Heinz Hofmann, Table of n, a(n) for n = 1..2329

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

Adjacent sequences: A366593 A366594 A366595 * A366597 A366598 A366599

Keyword

nonn,base,easy

Author

Kritsada Moomuang, Oct 14 2023

Status

approved