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%I #40 Jul 10 2014 12:22:22
%S 9175,9351,17676,24826,26038,28612,38026,38158,46212,46927,48247,
%T 56473,61863,63075,63898,65649,75063,75195,83425,83964,85284,91750,
%U 93510,100935
%N Integers n not of form 3m+2 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+2 then n*10^k+1 is always divisible by 3. The sequence is a base 10 variant of provable Sierpiński numbers (A076336). It is currently unknown whether 7666*10^k+1 is always composite but based on heuristics it probably has large undiscovered primes. 7666 is the only remaining base 10 Sierpiński candidate below 9175. - _Jens Kruse Andersen_, Jul 09 2014
%H A. Brunner, C. Caldwell, D. Krywaruczensko, C. Lownsdale, <a href="http://www.utm.edu/staff/caldwell/preprints/2to100.pdf">Generalized Sierpiński Numbers Base b</a> (has a typo in covering set for 9175, base 10. - _Jens Kruse Andersen_, Jul 09 2014)
%F For n>24 a(n) = a(n-24) + 111111.
%e 9175*10^k+1 is divisible by 11 for k of form 6m+1, 6m+3, 6m+5, by 37 for k of form 6m (and also 6m+3), by 13 for 6m+2, and by 7 for 6m+4. 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 i
%o DIM k,1
%o DIM n
%o OPENFILEOUT myf,a(n).txt
%o LABEL loop1
%o SET k,k+1
%o SET n,0
%o LABEL a
%o SET n,n+1
%o IF n>500 THEN GOTO b
%o SET i,k*(10^n)+1
%o IF i%3==0 THEN GOTO a
%o IF i%7==0 THEN GOTO a
%o IF i%11==0 THEN GOTO a
%o IF i%13==0 THEN GOTO a
%o IF i%37==0 THEN GOTO a
%o GOTO loop1
%o LABEL b
%o WRITE myf,k
%o GOTO loop1
%Y Cf. A076336, A076337, A243974, A244070.
%K nonn
%O 1,1
%A _Pierre CAMI_, Jun 16 2014
%E Definition corrected by _Jens Kruse Andersen_, Jul 09 2014
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