A277288 Positive integers n such that n | (3^n + 5).

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

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..14.

Example

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

Prog

(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

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).

Sequence in context: A227403 A156736 A334247 * A296412 A296410 A006266

Adjacent sequences: A277285 A277286 A277287 * A277289 A277290 A277291

Keyword

nonn,more

Author

Seiichi Manyama, Oct 09 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

Status

approved