A277340 Positive integers n such that n | (3^n + 11).

1, 2, 4, 7, 10, 92, 1099, 29530, 281473, 657892, 3313964, 9816013, 18669155396, 94849225930, 358676424226, 957439868543, 1586504109310, 41431374800470, 241469610359708, 256165266592379

Offset: 1

Author

Seiichi Manyama, Oct 09 2016

Keywords

• nonn

Comments

No other terms below 10^15. Some larger terms: 9151612250553176993, 1401778935853533028413047652833, 5645122353966835994338815444821661584288016927879134, 313*(3^626+11)/6562567821545333606830 (280 digits). - Max Alekseyev, Oct 14 2016

Examples

			3^10 + 11 = 59060 = 10 * 5906, so 10 is a term.
		

Crossrefs

Solutions to 3^n == k (mod n): this sequence (k=-11), A277289 (k=-7), A277288 (k=-5), A015973 (k=-2), A015949 (k=-1), A067945 (k=1), A276671 (k=2), A276740 (k=5), A277126 (k=7), A277274 (k=11).

Programs

PARI

is(n)=Mod(3,n)^n==-11; \\ Joerg Arndt, Oct 10 2016

Python

A277340_list = [1,2,4,7,10]+[n for n in range(11,10**6) if pow(3,n,n)==n-11] # Chai Wah Wu, Oct 11 2016

Extensions

a(13)-a(14) from Chai Wah Wu, Oct 12 2016

a(15)-a(20) from Max Alekseyev, Oct 14 2016