cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-8 of 8 results.

A015973 Positive integers n such that n | (3^n + 2).

Original entry on oeis.org

1, 5, 77, 278377, 3697489, 219596687717, 56865169816619
Offset: 1

Views

Author

Robert G. Wilson v

Keywords

Comments

No other terms below 10^15. Some larger term: 3142423971953435020522506484187. - Max Alekseyev, Aug 04 2011

Crossrefs

Cf. A015940, A050259, A123062
Solutions to 3^n == k (mod n): A277340 (k=-11), A277289 (k=-7), A277288 (k=-5), this sequence (k=-2), A015949 (k=-1), A067945 (k=1), A276671 (k=2), A276740 (k=5), A277126 (k=7), A277274 (k=11).

Extensions

a(1)=1 prepended and a(6)-a(7) added by Max Alekseyev, Aug 04 2011

A276740 Numbers n such that 3^n == 5 (mod n).

Original entry on oeis.org

1, 2, 4, 76, 418, 1102, 4687, 7637, 139183, 2543923, 1614895738, 9083990938, 23149317409, 497240757797, 4447730232523, 16000967516764, 65262766108619, 141644055557882
Offset: 1

Views

Author

Dmitry Ezhov, Sep 16 2016

Keywords

Comments

No other terms below 10^15. Some larger terms: 194995887252090239, 2185052151122686482926861593785262. - Max Alekseyev, Oct 13 2016

Examples

			3 == 5 (mod 1), so 1 is a term;
9 == 5 (mod 2), so 2 is a term.

Crossrefs

Cf. A066601.
Solutions to 3^n == k (mod n): A277340 (k=-11), A277289 (k=-7), A277288 (k=-5), A015973 (k=-2), A015949 (k=-1), A067945 (k=1), A276671 (k=2), this sequence (k=5), A277628 (k=6), A277126 (k=7), A277630 (k=8), A277274 (k=11).

Programs

  • Mathematica
    Select[Range[10^7], PowerMod[3, #, #] == Mod[5, #] &] (* Michael De Vlieger, Sep 26 2016 *)
  • PARI
    isok(n) = Mod(3, n)^n == Mod(5, n); \\ Michel Marcus, Sep 17 2016
  • Python
    A276740_list = [1,2,4]+[n for n in range(5,10**6) if pow(3,n,n) == 5] # Chai Wah Wu, Oct 04 2016

Extensions

a(11)-a(13) from Chai Wah Wu, Oct 05 2016
a(14) from Lars Blomberg, Oct 12 2016
a(15)-a(18) from Max Alekseyev, Oct 13 2016
a(12) was missing Robert G. Wilson v, Oct 19 2016

A277126 Positive integers n such that 3^n == 7 (mod n).

Original entry on oeis.org

1, 2, 295, 883438, 252027511, 7469046275, 26782373099, 53191768475, 55246802458, 819613658855, 893727887879978
Offset: 1

Views

Author

Seiichi Manyama, Oct 06 2016

Keywords

Comments

No other terms below 10^15. A larger term: 9135884036634915191945452485106476242. - Max Alekseyev, Oct 12 2016
Terms are not divisible by 127 (Alekseyev 2016).

Examples

			3 == 7 mod 1, so 1 is a term;
9 == 7 mod 2, so 2 is a term.

References

  • M. A. Alekseyev. "Problem 4101". Crux Mathematicorum 42:1 (2016), 28.

Crossrefs

Solutions to 3^n == k (mod n): A277340 (k=-11), A277289 (k=-7), A277288 (k=-5), A015973 (k=-2), A015949 (k=-1), A067945 (k=1), A276671 (k=2), A276740 (k=5), this sequence (k=7), A277274 (k=11).

Programs

Extensions

a(5) from Joerg Arndt, Oct 06 2016
a(6)-a(11) from Max Alekseyev, Oct 12 2016

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

Original entry on oeis.org

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

Views

Author

Seiichi Manyama, Oct 09 2016

Keywords

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

A277289 Positive integers n such that n | (3^n + 7).

Original entry on oeis.org

1, 2, 4, 5, 8, 25, 44, 4664, 6568, 1353025, 2919526, 5709589, 7827725, 64661225, 85132756, 153872408, 743947534, 34304296003, 38832409867, 40263727492, 1946603375348, 2469908330348, 64471909888247, 274267749806485, 888906849689897, 896501949422459
Offset: 1

Views

Author

Seiichi Manyama, Oct 09 2016

Keywords

Comments

No other terms below 10^15. - Max Alekseyev, Oct 14 2016
492385451091805616444 is a term.

Examples

			3^25 + 7 = 847288609450 = 25 * 33891544378, so 25 is a term.

Crossrefs

Solutions to 3^n == k (mod n): A277340 (k=-11), this sequence (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==-7; \\ Joerg Arndt, Oct 09 2016
  • Python
    A277289_list = [1,2,4,5]+[n for n in range(6,10**6) if pow(3,n,n)==n-7] # Chai Wah Wu, Oct 12 2016

Extensions

a(17) from Joerg Arndt, Oct 09 2016
a(18)-a(20) from Chai Wah Wu, Oct 12 2016
a(21)-a(26) from Max Alekseyev, Oct 14 2016

A277274 Positive integers n such that 3^n == 11 (mod n).

Original entry on oeis.org

1, 2, 1162, 1692934, 3851999, 274422823, 14543645261, 492230729674, 773046873382, 13010754158393, 31446154470014, 583396812890467, 598371102650063
Offset: 1

Views

Author

Seiichi Manyama, Oct 08 2016

Keywords

Comments

No other terms below 10^15. Some larger terms: 38726095838775708310162, 2682806839696008709567739369. - Max Alekseyev, Oct 12 2016

Examples

			3 == 11 mod 1, so 1 is a term.
9 == 11 mod 2, so 2 is a term.

Crossrefs

Solutions to 3^n == k (mod n): A277340 (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), this sequence (k=11).

Programs

  • Mathematica
    k = 3; lst = {1, 2}; While[k < 12000000001, If[ PowerMod[3, k, k] == 11, AppendTo[lst, k]]; k++]; lst (* Robert G. Wilson v, Oct 08 2016 *)

Extensions

a(7)-a(13) from Max Alekseyev, Oct 12 2016

A277628 Positive integers n such that 3^n == 6 (mod n).

Original entry on oeis.org

1, 3, 21, 936340943, 10460353197, 9374251222371, 23326283250291, 615790788171551
Offset: 1

Views

Author

Dmitry Ezhov, Oct 24 2016

Keywords

Comments

No other terms below 10^15. - Max Alekseyev, Sep 12 2017

Crossrefs

Solutions to 3^n == k (mod n): A277340 (k=-11), A277289 (k=-7), A277288 (k=-5), A015973 (k=-2), A015949 (k=-1), A067945 (k=1), A276671 (k=2), A276740 (k=5), this sequence (k=6), A277126 (k=7), A277630 (k=8), A277274 (k=11).

Programs

  • PARI
    isok(n) = Mod(3, n)^n == Mod(6, n);

Extensions

a(6)-a(8) from Max Alekseyev, Sep 12 2017

A277630 Positive integers n such that 3^n == 8 (mod n).

Original entry on oeis.org

1, 5, 2352527, 193841707, 17126009179703, 380211619942943
Offset: 1

Views

Author

Dmitry Ezhov, Oct 24 2016

Keywords

Comments

No other terms below 10^15. - Max Alekseyev, Sep 13 2017

Crossrefs

Solutions to 3^n == k (mod n): A277340 (k=-11), A277289 (k=-7), A277288 (k=-5), A015973 (k=-2), A015949 (k=-1), A067945 (k=1), A276671 (k=2), A276740 (k=5), A277628 (k=6), A277126 (k=7), this sequence (k=8), A277274 (k=11).

Programs

  • PARI
    isok(n) = Mod(3, n)^n == Mod(8, n);

Extensions

a(5)-a(6) established by Max Alekseyev, Sep 13 2017
Showing 1-8 of 8 results.

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