A232769 Numbers n not divisible by 9 such that n divides 10^n - 1 (A014950).

1, 3, 111, 4107, 151959, 5622483, 22494039, 208031871, 225121209, 832279443, 7697179227, 8329484733, 27486820443, 30794339391, 92366302683, 123199851603, 230915528769, 284795631399, 308190935121, 1017012356391

Offset: 1

Author

Hans Havermann and Robert G. Wilson v, Nov 29 2013

Keywords

• nonn

Comments

The above terms reduced modulo 9 yield: 1, 3, 3, 3, 3, 3, 6, 3, 6, 6, 3, 6, 3, 6, 3, 3, 3, 3, 6, 3, 6, …, .

The only primes less than a billion which can divide members of this sequence are 3, 37, 5477, 607837, 1519591, 2028119, 15195911, 18235093, 44988079, 74202397, 247629013, 337349203, 395397319, 462411133, and 674699071. - Charles R Greathouse IV, Dec 03 2013

Links

• Ray Chandler, Table of n, a(n) for n = 1..55

Crossrefs

Cf. A014950.

Programs

Mathematica

k = 3; lst = {1}; While[k < 10^10 + 1, If[ PowerMod[10, k, k] == 1, AppendTo[ lst, k]; Print@ k]; k += 3; If[ PowerMod[ 10, k, k] == 1, AppendTo[ lst, k]; Print@ k]; k += 6]; lst

PARI

is(n)=n%9 && Mod(10,n)^n==1 \\ Charles R Greathouse IV, Dec 03 2013

PARI

forstep(n=1,1e8,[2, 4, 4, 2, 4, 2, 2, 2, 6, 2, 2, 4, 2, 2, 2, 4, 2, 2, 2, 4, 2, 2, 6, 2, 2, 2, 4, 2, 4, 4, 2, 2], if(Mod(10,n)^n==1,print1(n", "))) \\ Charles R Greathouse IV, Dec 03 2013

Extensions

a(22)-a(26) from Ray Chandler, Dec 11 2013

B-file extended through a(55) by Ray Chandler, Dec 24 2013