A058046 -id:A058046 - cp's OEIS frontend

A104745 a(n) = 5^n + n.

1, 6, 27, 128, 629, 3130, 15631, 78132, 390633, 1953134, 9765635, 48828136, 244140637, 1220703138, 6103515639, 30517578140, 152587890641, 762939453142, 3814697265643, 19073486328144, 95367431640645, 476837158203146, 2384185791015647, 11920928955078148, 59604644775390649

Offset: 0

Zak Seidov, Mar 23 2005

Numbers m=5^n+n such that equation x=5^(m-x) has solution x=5^n, see A104744.
No primes of the form 5^n+n for n < 7954. - Thomas Ordowski, Oct 28 2013
a(7954) is prime (5560 digits). - Thomas Ordowski, May 07 2015

Vincenzo Librandi, Table of n, a(n) for n = 0..300
Factordb, 5^7954 + 7954.
Index entries for linear recurrences with constant coefficients, signature (7,-11,5).

Cf. A006127, A058046, A081552, A093324, A104743, A104744, A158879, A181572.

I:=[1, 6, 27]; [n le 3 select I[n] else 7*Self(n-1)-11*Self(n-2) +5*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Jun 16 2013

g:=1/(1-5*z): gser:=series(g, z=0, 43): seq(coeff(gser, z, n)+n, n=0..31); # Zerinvary Lajos, Jan 09 2009

Table[5^n+n,{n,0,40}] (* Vladimir Joseph Stephan Orlovsky, May 19 2011 *)
CoefficientList[Series[(1 - x - 4 x^2) / ((1 - 5 x) (1 - x)^2), {x, 0, 30}], x] (* Vincenzo Librandi, Jun 16 2013 *)
LinearRecurrence[{7,-11,5},{1,6,27},30] (* Harvey P. Dale, Dec 03 2017 *)

a(n)=5^n+n \\ Charles R Greathouse IV, Oct 07 2015

From Vincenzo Librandi, Jun 16 2013: (Start)
G.f.: (1-x-4*x^2)/((1-5*x)*(1-x)^2).
a(n) = 7*a(n-1) - 11*a(n-2) + 5*a(n-3). (End)
E.g.f.: exp(x)*(exp(4*x) + x). - Elmo R. Oliveira, Mar 05 2025

More terms from Jonathan R. Love (japanada11(AT)yahoo.ca), Mar 09 2007

A224470 Numbers k such that 7^k - k is prime.

Original entry on oeis.org

2, 6, 8, 12, 44, 48, 512, 1088, 1104, 6038

Offset: 1

Alex Ratushnyak, Apr 06 2013

a(11) > 92000. - Giovanni Resta, Apr 08 2013

a(11) > 2*10^5. - Robert Price, Feb 11 2014

Cf. A048744, A058037, A057908, A058046, A058829, A224468.

forstep(n=2,10^4,2,if(ispseudoprime(7^n-n),print1(n,", "))); /* Joerg Arndt, Apr 07 2013 */

A224471 Numbers k such that 8^k - k is prime.

Original entry on oeis.org

1, 3, 37, 45, 597, 1131, 14203, 112539

Offset: 1

Alex Ratushnyak, Apr 06 2013

a(8) > 41000. - Giovanni Resta, Apr 07 2013

a(9) > 2*10^5. - Robert Price, Jan 19 2014

Cf. A048744, A058037, A057908, A058046, A058829, A224470, A224469, A224469.

import java.math.BigInteger;
public class A224471 {
  public static void main (String[] args) {
    BigInteger b8 = BigInteger.valueOf(8);
    BigInteger m = BigInteger.valueOf(64);
    for(long n=1; ; n+=2) {
        BigInteger b = b8.subtract(BigInteger.valueOf(n));
        if (b.isProbablePrime(2)) {
            if (b.isProbablePrime(80))
                System.out.printf("%d\n", n);
        }
        b8 = b8.multiply(m);
    }
  }
}

forstep(n=1,10^4,2,if(ispseudoprime(8^n-n),print1(n,", "))); /* Joerg Arndt, Apr 07 2013 */

a(7) from Giovanni Resta, Apr 07 2013

a(8) from Robert Price, Jan 19 2014

A273940 Primes of the form 5^m - m.

Original entry on oeis.org

23, 15619, 244140613

Offset: 1

Vincenzo Librandi, Jun 05 2016

Corresponding values of m are given in A058046.

The next term has 254 digits.

Amiram Eldar, Table of n, a(n) for n = 1..5

Primes of the form k^m - m: A081296 (k=2), A224420 (k=3), A224451 (k=4), this sequence (k=5), A273941 (k=6), A224468 (k=7), A224469 (k=8).

Cf. A024050, A058046.

[a: n in [0..400] | IsPrime(a) where a is 5^n-n];

Select[Table[5^n - n, {n, 400}], PrimeQ]

forstep(n=2,1e4,2, if(ispseudoprime(t=5^n-n), print1(t", "))) \\ Charles R Greathouse IV, Jun 08 2016

a(n) = A024050(A058046(n)). - Amiram Eldar, Jul 27 2025

A382786 Numbers k such that 5^k + k is prime.

Original entry on oeis.org

7954, 22102, 33054, 135156

Offset: 1

Nico Puada, Apr 24 2025

All terms must end in the digit 2, 4, 6 or 8, otherwise 5^k + k is divisible by 2 or 5, which is not prime. - Jakub Buczak, May 04 2025

Cf. A104745, A052007, A057900, A057909, A058046.

Select[Range[35000], PrimeQ[5^# + #] &] (* Nico Puada, Apr 24 2025 *)

a(4) corrected by Jakub Buczak, May 04 2025

A224506 Numbers k such that 9^k - k is prime.

Original entry on oeis.org

2, 70, 88, 6562, 9100, 11758, 34334, 39212, 120590

Offset: 1

Alex Ratushnyak, Apr 08 2013

a(7) > 20000. - Giovanni Resta, Apr 09 2013

a(10) > 2*10^5. - Robert Price, Mar 12 2014

Cf. A048744, A058037, A057908, A058046, A058829, A224470, A224471.

Select[Range[1000], PrimeQ[9^# - #] &] (* Alonso del Arte, Apr 11 2013 *)

is(n)=ispseudoprime(9^n-n) \\ Charles R Greathouse IV, Jun 13 2017

a(6) from Giovanni Resta, Apr 09 2013

a(7)-a(9) from Robert Price, Mar 12 2014

cp's OEIS Frontend

A104745 a(n) = 5^n + n.

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A224470 Numbers k such that 7^k - k is prime.

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A224471 Numbers k such that 8^k - k is prime.

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A273940 Primes of the form 5^m - m.

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A382786 Numbers k such that 5^k + k is prime.

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A224506 Numbers k such that 9^k - k is prime.

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