A277288 Positive integers k such that k divides 3^k + 5.

1, 2, 14, 1978, 38209, 4782974, 9581014, 244330711, 365496202, 1661392258, 116084432414, 288504187458218, 490179448388654, 802245996685561

Offset: 1

Author

Seiichi Manyama, Oct 09 2016

Keywords

• nonn
• more

Comments

No other terms below 10^15. Some larger terms: 79854828136468902206, 3518556634988844968631084847788071912030455376274045370172567094578. - Max Alekseyev, Oct 14 2016

Examples

			3^14 + 5 = 4782974 = 14 * 341641, so 14 is a term.
		

Crossrefs

Solutions to 3^n == k (mod n): A277340 (k=-11), A277289 (k=-7), this sequence (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==-5; \\ Joerg Arndt, Oct 09 2016

Python

A277288_list = [1,2]+[n for n in range(3,10**6) if pow(3,n,n)==n-5] # Chai Wah Wu, Oct 09 2016

Sage

def A277288_list(search_limit):
    n, t, r = 1, Integer(3), [1]
    while n < search_limit:
        n += 1
        t *= 3
        if n.divides(t+5): r.append(n)
    return r # Peter Luschny, Oct 10 2016

Extensions

a(9) from Joerg Arndt, Oct 09 2016

a(10) from Chai Wah Wu, Oct 09 2016

a(11)-a(14) from Max Alekseyev, Oct 14 2016