A243974 Integers n not of form 3m+1 such that for any integer k>0, n*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

Offset

1,1

Comments

For n>24 a(n) = a(n-24) + 111111, the first 24 values are in the data.

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

Links

Table of n, a(n) for n=1..24.

Formula

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

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)
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

Author

Pierre CAMI, Jun 16 2014

Extensions

Definition corrected by Jens Kruse Andersen, Jul 09 2014

Status

approved