

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
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OFFSET

1,1


COMMENTS

For n>24 a(n) = a(n24) + 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

Table of n, a(n) for n=1..24.
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(n24) + 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

Cf. A076336, A076337, A243974, A244070.
Sequence in context: A210140 A232759 A250149 * A231424 A234887 A251902
Adjacent sequences: A243966 A243967 A243968 * A243970 A243971 A243972


KEYWORD

nonn


AUTHOR

Pierre CAMI, Jun 16 2014


EXTENSIONS

Definition corrected by Jens Kruse Andersen, Jul 09 2014


STATUS

approved



