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 }.

9175, 9351, 17676, 24826, 26038, 28612, 38026, 38158, 46212, 46927, 48247, 56473, 61863, 63075, 63898, 65649, 75063, 75195, 83425, 83964, 85284, 91750, 93510, 100935

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

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(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

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