A253211 -id:A253211 - cp's OEIS frontend

A144360 Primes of the form 8^k + 7. Also, primes of the form 64^m + 7.

71, 262151, 1073741831, 302231454903657293676551, 85070591730234615865843651857942052871, 23945242826029513411849172299223580994042798784118791, 25711008708143844408671393477458601640355247900524685364822023

Offset: 1

Reikku Kulon, Sep 18 2008

nonn

k=2m, since for odd k, 8^k + 7 is divisible by 3.
Prime numbers p in A144242 such that p-1 is the fourth a-gonal and seventh b-gonal number for some a and b. Namely, a = (8^k+14)/6 and b = (8^k + 41)/21.
This sequence appears to be a subset of A144313.
The next term has 178 digits. - Harvey P. Dale, Sep 03 2015

			71 - 1 = 70 is the fourth triskaidecagonal number and seventh pentagonal number.

Amiram Eldar, Table of n, a(n) for n = 1..10

Cf. A000040, A000668, A144231, A144232, A144233, A144234, A144236, A144242, A144245, A144246, A144247, A144313.

[a: n in [0..80] | IsPrime(a) where a is 8^n+7]; // Vincenzo Librandi, Aug 02 2017

Select[64^Range[40]+7,PrimeQ] (* Harvey P. Dale, Sep 03 2015 *)

a(n) = A253211(A217381(n)). - Amiram Eldar, Jul 23 2025

Edited by Max Alekseyev, Feb 17 2011

A253208 a(n) = 4^n + 3.

Original entry on oeis.org

4, 7, 19, 67, 259, 1027, 4099, 16387, 65539, 262147, 1048579, 4194307, 16777219, 67108867, 268435459, 1073741827, 4294967299, 17179869187, 68719476739, 274877906947, 1099511627779, 4398046511107, 17592186044419, 70368744177667, 281474976710659

Offset: 0

Vincenzo Librandi, Dec 29 2014

Subsequence of A226807.

Index entries for linear recurrences with constant coefficients, signature (5,-4).

Cf. A141725, A226807.

Cf. Numbers of the form k^n+k-1: A000057 (k=2), A168607 (k=3), this sequence (k=4), A242329 (k=5), A253209 (k=6), A253210 (k=7), A253211 (k=8), A253212 (k=9), A253213 (k=10).

Magma
```
[4^n+3: n in [0..30]];
```

Table[4^n + 3, {n, 0, 30}] (* or *) CoefficientList[Series[(4 - 13 x) / ((1 - x) (1 - 4 x)), {x, 0, 40}], x]

a(n)=4^n+3 \\ Charles R Greathouse IV, Oct 07 2015

G.f.: (4 - 13*x)/((1 - x)*(1 - 4*x)).
a(n) = 5*a(n-1) - 4*a(n-2) for n > 1.
From Elmo R. Oliveira, Nov 14 2023: (Start)
a(n) = 4*a(n-1) - 9 with a(0) = 4.
E.g.f.: exp(4*x) + 3*exp(x). (End)

A327468 Numbers m that divide 8^m + 7.

Original entry on oeis.org

1, 3, 5, 25, 519, 290502305, 821808425, 979288025, 982989263, 25783323897, 27771237541, 31045665345, 65130752425, 3708883906025, 15079242289703, 973336048301405

Offset: 1

Juri-Stepan Gerasimov, Oct 04 2019

Conjecture: For k > 1, k^m == 1-k (mod m) has an infinite number of positive solutions.
Integer m not divisible by 3 is a term if and only if 3m is a term of A240941. - Max Alekseyev, Feb 07 2024
Also terms 930486448009391617725 and 21036656390681764555645540794214294457925. - Giovanni Resta, Oct 04 2019
Other terms 71245661271703622047, 7093208961478946798805, 7807963392818324067361574236385. - Max Alekseyev, Feb 07 2024

Solutions to k^m == 1-k (mod m): 1 (k = 1), A006521 (k = 2), A015973 (k = 3), A327840 (k = 4), A123047 (k = 5), A327943 (k = 6), A328033 (k = 7), this sequence (k = 8).

Cf. A240941, A253211.

[m: m in [1..7] | (8^m + 7) mod m eq 0] cat [m: m in [8..10^8] | Modexp(8, m, m) + 7 eq m]; // Jon E. Schoenfield, Oct 05 2019

isok(n) = Mod(8, n)^n==-7; \\ Michel Marcus, Oct 05 2019

a(10)-a(13) from Giovanni Resta, Oct 04 2019

a(14)-a(16) from Max Alekseyev, Feb 07 2024

cp's OEIS Frontend

A144360 Primes of the form 8^k + 7. Also, primes of the form 64^m + 7.

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A253208 a(n) = 4^n + 3.

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A327468 Numbers m that divide 8^m + 7.

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