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A303608 Repunit pseudoprimes: composite numbers n such that (10^n - 1)/9 == 1 (mod n). 2
10, 55, 91, 259, 370, 385, 451, 481, 505, 703, 715, 1045, 1105, 1729, 2035, 2465, 2821, 2981, 3367, 4141, 4187, 5005, 5461, 6533, 6541, 6565, 6601, 7471, 7777, 8149, 8401, 8695, 8905, 8911, 10001, 10585, 11111, 12403, 13366, 13981, 14245, 14645, 14701, 14911, 15211, 15841, 18685 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Composite numbers n such that 10^n == 10 (mod 9n).

If n is a term, then so is (10^n - 1)/9. Thus, the sequence is infinite.

No terms are divisible by 3. - Robert Israel, May 28 2018

LINKS

Robert Israel, Table of n, a(n) for n = 1..4130

EXAMPLE

(10^10 - 1)/9 = 1111111111 == 1 (mod 10), so the composite 10 is a term.

Equivalently, we have the congruence 10^10 == 10 (mod 9*10).

MAPLE

filter:=  n -> n mod 3 <> 0 and (10&^n - 10) mod n = 0\ and not isprime(n):

select(filter, [$4..10^5]); # Robert Israel, May 28 2018

MATHEMATICA

Select[Range@ 20000, ! PrimeQ@# && PowerMod[10, #, 9 #] == 10 &] (* Robert G. Wilson v, Apr 28 2018 *)

PROG

(PARI) isok(n) = (n>1) && !isprime(n) && Mod(10, 9*n)^n == 10; \\ Michel Marcus, Apr 28 2018

CROSSREFS

A000864 is a subsequence.

Composite numbers in A067934. - Michel Marcus, Apr 27 2018

Sequence in context: A222539 A219623 A284757 * A139610 A088404 A119334

Adjacent sequences:  A303605 A303606 A303607 * A303609 A303610 A303611

KEYWORD

nonn

AUTHOR

Thomas Ordowski, Apr 27 2018

EXTENSIONS

a(4) onward from Robert G. Wilson v, Apr 27 2018

STATUS

approved

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Last modified August 24 22:49 EDT 2019. Contains 326314 sequences. (Running on oeis4.)