A074507 -id:A074507 - cp's OEIS frontend

A076515 Numbers k such that 1 + 3^k + 5^k is prime.

0, 12, 36, 48, 72, 120, 605376

Offset: 1

Zak Seidov, Oct 17 2002

Next term, if it exists, is greater than 35000. - Vaclav Kotesovec, Jan 26 2016
No more terms up to 75000 (previous range rechecked). All terms are multiples of 12: if k > 0 is not a multiple of 12, 1 + 3^k + 5^k is divisible by 3, 5 or 7. - Rick L. Shepherd, Aug 06 2017
Next term, if it exists, is greater than 10^6. - Jon Grantham, Jul 29 2023

Cf. A008594, A074507, A268064, A268065, A268067.

[n: n in [0..1000]|IsPrime(3^n+5^n+1)] // Vincenzo Librandi, Jan 22 2011

A076515:=n->`if`(isprime(1+3^n+5^n), n, NULL): seq(A076515(n), n=0..200); # Wesley Ivan Hurt, Aug 06 2017

Do[ If[ PrimeQ[1 + 3^n + 5^n], Print[n]], {n, 0, 3500, 2}]
Select[Range[0,5000],PrimeQ[1+3^#+5^#]&] (* Harvey P. Dale, Mar 09 2012 *)

lista(nn) = for(n=0, nn, if(ispseudoprime(1 + 3^n + 5^n), print1(n, ", "))); \\ Altug Alkan, Jan 25 2016

a(7) from Jon Grantham, Jul 29 2023

A134006 a(n) = 1^n + 3^n + 5^n + 7^n.

Original entry on oeis.org

4, 16, 84, 496, 3108, 20176, 134004, 903856, 6161988, 42326416, 292299924, 2026332016, 14085959268, 98111307856, 684331371444, 4778093436976, 33385561506948, 233393582580496, 1632228682596564, 11417969833962736

Offset: 0

Artur Jasinski, Oct 01 2007

nonn

			a(3)=84 because 1^2+3^2+5^2+7^2=84.

Vincenzo Librandi, Table of n, a(n) for n = 0..300
T. A. Gulliver, Divisibility of sums of powers of odd integers, Int. Math. For. 5 (2010) 3059-3066, eq. 6.
Index entries for linear recurrences with constant coefficients, signature (16, -86, 176, -105).

Cf. A034472, A074507, A134007.

[1^n + 3^n + 5^n + 7^n: n in [0..30]]; // Vincenzo Librandi, Jun 20 2011

Mathematica
```
Table[1^n+3^n+5^n+7^n,{n,0,30}]
```

{a(n) = 1^n + 3^n + 5^n + 7^n}; /* Michael Somos, Jun 29 2017 */

a(n) = 15*a(n-1) - 71*a(n-2) + 105*a(n-3) - 48.
a(n) = A074507(n) + A000420(n). - Michel Marcus, Nov 07 2013
G.f.: 1 / (1 - x) + 1 / (1 - 3*x) + 1 / (1 - 5*x) + 1 / (1 - 7*x), E.g.f.: exp(x) + exp(3*x) + exp(5*x) + exp(7*x). - Michael Somos, Jun 29 2017

A134007 a(n) = 1^n + 3^n + 5^n + 7^n + 9^n.

Original entry on oeis.org

5, 25, 165, 1225, 9669, 79225, 665445, 5686825, 49208709, 429746905, 3779084325, 33407391625, 296515495749, 2639977136185, 23561123826405, 210669225531625, 1886405750358789, 16910575282247065, 151726863979595685

Offset: 0

Artur Jasinski, Oct 01 2007

			a(3)=165 because 1^2 + 3^2 + 5^2 + 7^2 + 9^2 = 165.

Vincenzo Librandi, Table of n, a(n) for n = 0..300
T. A. Gulliver, Divisibility of sums of powers of odd integers, Int. Math. For. 5 (2010) 3059-3066, eq. 6.
Index entries for linear recurrences with constant coefficients, signature (25, -230, 950, -1689, 945).

Cf. A034472, A074507, A134006.

[1^n + 3^n + 5^n + 7^n + 9^n: n in [0..20]]; // Vincenzo Librandi, Jun 20 2011

Mathematica
```
Table[1^n+3^n+5^n+7^n+9^n,{n,0,30}]
```

a(n) = 24*a(n-1) - 206*a(n-2) + 744*a(n-3) - 945*a(n-4) + 384.
G.f.: -(5 - 100*x + 690*x^2 - 1900*x^3 + 1689*x^4)/((-1+x)*(3*x-1)*(9*x-1)*(7*x-1)*(5*x-1)). - R. J. Mathar, Nov 14 2007
a(n) = A134006(n) + A001019(n). - Michel Marcus, Nov 07 2013

A081508 Primes of form 1 + 3^k + 5^k.

Original entry on oeis.org

3, 244672067, 14551915378461487103639747, 3552713678880267372432493847753987, 211758236813575107295480170109084902352995775163267

Offset: 1

Labos Elemer, Apr 15 2003

nonn

Amiram Eldar, Table of n, a(n) for n = 1..6

Cf. A074507, A076515, A277122.

Do[s=1^w+3^w+5^w; If[IntegerQ[w/100], Print[{w}]]; If[PrimeQ[s], Print[{w, s}]], {w, 0, 1000}]

lista(kmax) = {my(p); for(k = 0, kmax, p = 1 + 3^k + 5^k; if(isprime(p), print1(p, ", ")));} \\ Amiram Eldar, Aug 11 2024

a(n) = A074507(A076515(n)). - Amiram Eldar, Aug 11 2024

A134008 a(n) = 1^n + 3^n + 5^n + 7^n + 9^n + 11^n.

Original entry on oeis.org

6, 36, 286, 2556, 24310, 240276, 2437006, 25173996, 263567590, 2787694596, 29716508926, 318719062236, 3434943872470, 37162689280116, 403310957409646, 4387917394947276, 47836135613930950, 522357603781540836

Offset: 0

Artur Jasinski, Oct 01 2007

nonn

			a(3)=286 because 1^2 + 3^2 + 5^2 + 7^2 + 9^2 + 11^2 = 286.

Vincenzo Librandi, Table of n, a(n) for n = 0..300
T. A. Gulliver, Divisibility of sums of powers of odd integers, Int. Math. For. 5 (2010) 3059-3066, eq. 6.
Index entries for linear recurrences with constant coefficients, signature (36,-505,3480,-12139,19524,-10395).

Cf. A034472, A074507, A134006, A134007.

[1^n + 3^n + 5^n + 7^n + 9^n + 11^n: n in [0..20]]; // Vincenzo Librandi, Jun 20 2011

Table[1^n+3^n+5^n+7^n+9^n+11^n,{n,0,30}]
Join[{6},Table[Total[Range[1,11,2]^n],{n,20}]] (* or *) LinearRecurrence[ {36,-505,3480,-12139,19524,-10395},{6,36,286,2556,24310,240276},20] (* Harvey P. Dale, Apr 20 2015 *)

a(n) = 35*a(n-1) - 470*a(n-2) + 3010*a(n-3) - 9129*a(n-4) + 10395*a(n-5) - 3840.
G.f.: -2*(6*x-1)*(1627*x^4 - 1752*x^3 + 578*x^2 - 72*x + 3)/((-1+x)*(9*x-1)*(7*x-1)*(3*x-1)*(5*x-1)*(11*x-1)). - R. J. Mathar, Nov 14 2007
a(n) = 36*a(n-1) - 505*a(n-2) + 3480*a(n-3) - 12139*a(n-4) +  19524*a(n-5) - 10395*a(n-6); a(0)=6, a(1)=36, a(2)=286, a(3)=2556, a(4)=24310, a(5)=240276. - Harvey P. Dale, Apr 20 2015

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A076515 Numbers k such that 1 + 3^k + 5^k is prime.

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A134006 a(n) = 1^n + 3^n + 5^n + 7^n.

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A134007 a(n) = 1^n + 3^n + 5^n + 7^n + 9^n.

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A081508 Primes of form 1 + 3^k + 5^k.

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PARI

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A134008 a(n) = 1^n + 3^n + 5^n + 7^n + 9^n + 11^n.

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