A243974 Integers j not of form 3m+1 such that for any integer k>0, j*10^k-1 has a divisor in the set { 7, 11, 13, 37 }.

10176, 17601, 19361, 25827, 27147, 27686, 35916, 36048, 45462, 47213, 48036, 49248, 54638, 62864, 64184, 64899, 72953, 73085, 82499, 85073, 86285, 93435, 101760, 101936, 121287, 128712, 130472, 136938, 138258, 138797, 147027, 147159, 156573, 158324, 159147, 160359

Offset

1,1

Comments

For n > 24, a(n) = a(n-24) + 111111.

If j is of form 3m+1 then j*10^k-1 is always divisible by 3. - Jens Kruse Andersen, Jul 09 2014

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1).

Formula

a(n) = a(n-24) + 111111 for n > 24.

Example

10176*10^k-1 is divisible by 11 for k of form 6m, 6m+2, 6m+4, by 7 for k of form 6m+1, by 37 for 6m+3 (and also 6m), and by 13 for 6m+5. This covers all k. {7, 11, 13, 37} is called a covering set. - Jens Kruse Andersen, Jul 09 2014

Prog

(PFGW)
SCRIPT
DIM k, 0
DIM n
DIMS t
OPENFILEOUT myf, res.txt
LABEL loop1
SET k, k+1
SET n, 0
LABEL loop2
SET n, n+1
IF n>500 THEN GOTO a
IF (k*10^n-1)%7==0 THEN GOTO loop2
IF (k*10^n-1)%11==0 THEN GOTO loop2
IF (k*10^n-1)%13==0 THEN GOTO loop2
IF (k*10^n-1)%37==0 THEN GOTO loop2
GOTO loop1
LABEL a
WRITE myf, k
PRINT k
GOTO loop1

Crossrefs

Cf. A076337, A243969, A243974, A244070, A244071, A244072, A244073, A244074, A244076.

Sequence in context: A231030 A323486 A153139 * A251274 A184205 A128878

Adjacent sequences: A243971 A243972 A243973 * A243975 A243976 A243977

Keyword

nonn,easy

Author

Pierre CAMI, Jun 16 2014

Extensions

Definition corrected by Jens Kruse Andersen, Jul 09 2014

a(25) onward from Andrew Howroyd, Feb 08 2026

Status

approved