A243974 - OEIS

%I #54 Apr 25 2016 11:50:02

%S 10176,17601,19361,25827,27147,27686,35916,36048,45462,47213,48036,

%T 49248,54638,62864,64184,64899,72953,73085,82499,85073,86285,93435,

%U 101760,101936

%N 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 }.

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

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

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

%e 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

%o (PFGW & SCRIPT)

%o SCRIPT

%o DIM k,0

%o DIM n

%o DIMS t

%o OPENFILEOUT myf,res.txt

%o LABEL loop1

%o SET k,k+1

%o SET n,0

%o LABEL loop2

%o SET n,n+1

%o IF n>500 THEN GOTO a

%o IF (k*10^n-1)%7==0 THEN GOTO loop2

%o IF (k*10^n-1)%11==0 THEN GOTO loop2

%o IF (k*10^n-1)%13==0 THEN GOTO loop2

%o IF (k*10^n-1)%37==0 THEN GOTO loop2

%o GOTO loop1

%o LABEL a

%o WRITE myf,k

%o PRINT k

%o GOTO loop1

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

%K nonn

%O 1,1

%A _Pierre CAMI_, Jun 16 2014

%E Definition corrected by _Jens Kruse Andersen_, Jul 09 2014