OFFSET
1,1
COMMENTS
For n > 24, a(n) = a(n-24) + 111111.
If j is of form 3m+2 then j*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
Andrew Howroyd, Table of n, a(n) for n = 1..1000
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)
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
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
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
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