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A243969 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 }. 6
9175, 9351, 17676, 24826, 26038, 28612, 38026, 38158, 46212, 46927, 48247, 56473, 61863, 63075, 63898, 65649, 75063, 75195, 83425, 83964, 85284, 91750, 93510, 100935 (list; graph; refs; listen; history; text; internal format)
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+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
LINKS
A. Brunner, C. Caldwell, D. Krywaruczensko, C. Lownsdale, Generalized Sierpiński Numbers Base b (has a typo in covering set for 9175, base 10. - Jens Kruse Andersen, Jul 09 2014)
FORMULA
For n>24 a(n) = a(n-24) + 111111.
EXAMPLE
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
PROG
(PFGW & SCRIPT)
SCRIPT
DIM i
DIM k, 1
DIM n
OPENFILEOUT myf, a(n).txt
LABEL loop1
SET k, k+1
SET n, 0
LABEL a
SET n, n+1
IF n>500 THEN GOTO b
SET i, k*(10^n)+1
IF i%3==0 THEN GOTO a
IF i%7==0 THEN GOTO a
IF i%11==0 THEN GOTO a
IF i%13==0 THEN GOTO a
IF i%37==0 THEN GOTO a
GOTO loop1
LABEL b
WRITE myf, k
GOTO loop1
CROSSREFS
Sequence in context: A210140 A232759 A250149 * A231424 A234887 A251902
KEYWORD
nonn
AUTHOR
Pierre CAMI, Jun 16 2014
EXTENSIONS
Definition corrected by Jens Kruse Andersen, Jul 09 2014
STATUS
approved

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Last modified July 14 12:26 EDT 2024. Contains 374318 sequences. (Running on oeis4.)