A220509 -id:A220509 - cp's OEIS frontend

A220511 a(n) = n^5 + 5*n + 5^n.

1, 11, 67, 383, 1669, 6275, 23431, 94967, 423433, 2012219, 9865675, 48989231, 244389517, 1221074483, 6104053519, 30518337575, 152588939281, 762940873067, 3814699155283, 19073488804319, 95367434840725, 476837162287331, 2384185796169367, 11920928961514583

Offset: 0

Jonathan Vos Post, Dec 15 2012

			a(1) = 1^5 + 5*1 + 5^1 = 11.
a(2) = 2^5 + 5*2 + 5^2 = 67.

Index entries for linear recurrences with constant coefficients, signature (11,-45,95,-115,81,-31,5).

Cf. A000351, A000584, A008587, A220425, A220509.

Table[n^5 + 5*n + 5^n, {n, 0, 30}] (* T. D. Noe, Dec 17 2012 *)
LinearRecurrence[{11,-45,95,-115,81,-31,5},{1,11,67,383,1669,6275,23431},30] (* Harvey P. Dale, Jun 03 2024 *)

makelist(n^5 + 5*n + 5^n,n,0,20); /* Martin Ettl, Jan 15 2013 */

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

a(n) = A000584(n) + A008587(n) + A000351(n).

G.f.: (29*x^6+30*x^5+459*x^4-46*x^3+9*x^2-1) / ((x-1)^6*(5*x-1)). - Colin Barker, May 09 2013

A220528 a(n) = n^7 + 7*n + 7^n.

Original entry on oeis.org

1, 15, 191, 2551, 18813, 94967, 397627, 1647135, 7862009, 45136639, 292475319, 1996813991, 13877119093, 96951759015, 678328486451, 4747732369423, 33233199005169, 232630924325999, 1628414210130607, 11398896079245015, 79792267577612141, 558545865884372695

Offset: 0

Jonathan Vos Post, Dec 15 2012

			a(1) = 1^7 + 7*1 + 7^1 = 15.
a(2) = 2^7 + 7*2 + 7^2 = 191.

Index entries for linear recurrences with constant coefficients, signature (15,-84,252,-462,546,-420,204,-57,7).

Cf. A000420, A001015, A008589, A220425, A220509, A220511, A220703.

Table[n^7 + 7*n + 7^n, {n, 0, 30}] (* T. D. Noe, Dec 17 2012 *)

makelist(n^7 + 7*n + 7^n,n,0,20); /* Martin Ettl, Jan 15 2013 */

a(n) = A001015(n) + A008589(n) + A000420(n).

G.f.: (55*x^8+546*x^7+8966*x^6+14692*x^5+6726*x^4-694*x^3-50*x^2-1) / ((x-1)^8*(7*x-1)). - Colin Barker, May 09 2013

A220653 a(n) = n^11 + 11*n + 11^n.

Original entry on oeis.org

1, 23, 2191, 178511, 4208989, 48989231, 364568683, 1996813991, 8804293561, 33739007399, 125937424711, 570623341343, 3881436747541, 36314872538111, 383799398753059, 4185897925275191, 45967322049616753, 505481300395601591, 5559981581902310911, 61159206938673444719

Offset: 0

Jonathan Vos Post, Dec 17 2012

This is to A220425 as 11 is to 2, to A220509 as 11 is to 3, to A220511 as 11 is to 5, and to A220528 as 11 is to 7.

The subsequence of primes begins: 23, 4185897925275191, see A220787 for the associated n.

			a(1) = 1^11 + 11*1 + 11^1 = 23.

Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1).

Cf. A008455, A008593, A001020, A220425, A220509, A220511, A220528, A220787.

Table[n^11 + 11*n + 11^n, {n, 0, 30}] (* T. D. Noe, Dec 17 2012 *)

A220653(n):=n^11+11*n+11^n$ makelist(A220653(n),n,0,20); /* Martin Ettl, Dec 17 2012 */

a(n) = A008455(n) + A008593(n) + A001020(n).

G.f.: (131*x^12 +21186*x^11 +1682460*x^10 +24070936*x^9 +104942001*x^8 +163196604*x^7 +91422264*x^6 +14484216*x^5 -518211*x^4 -131726*x^3 -1860*x^2 -1) / ((x -1)^12*(11*x -1)). - Colin Barker, May 09 2013

a(19) from Stefano Spezia, May 03 2025

A182127 Main diagonal T(n,n) of array T(k,n) = n-th value of m^prime(k) + m*prime(k) + prime(k)^m.

Original entry on oeis.org

1, 7, 67, 2551, 4208989, 1221074483, 16926683582407, 11398896079245015, 590295810437016637177, 4710128697246259342067579819, 10000000000000000819628286981111, 340039485861577398992584799927541447791, 176372588156290374069930689165295413889886285

Offset: 1

Jonathan Vos Post, Dec 19 2012

			The upper left corner of the matrix is:
.
k\n | 1   2     3       4        5         6
----+---------------------------------------
  1 | 1   5    12      23       40        67  (A220425)
  2 | 1   7    23      63      157       383  (A220509)
  3 | 1  11    67     383     1669      6275  (A220511)
  4 | 1  15   191    2551    18813     94967  (A220528)
  5 | 1  23  2191  178511  4208989  48989231  (A220653)

Cf. A220425, A220509, A220511, A220528, A220653.

A182127T := proc(n,k)
    p := ithprime(k) ;
    n^p+n*p+p^n ;
end proc:
A182127 := proc(n)
    A182127T(n-1,n) ;
end proc:
seq(A182127(n),n=1..13) ; # R. J. Mathar, Dec 22 2012

A209261 a(n) = n^13 + 13*n + 13^n.

Original entry on oeis.org

1, 27, 8387, 1596559, 67137477, 1221074483, 13065520903, 96951759015, 550571544713, 2552470327819, 10137858491979, 36314872538111, 130291290501709, 605750213184675, 4731091158953615, 53132088082450327, 669920208810550545

Offset: 0

Jonathan Vos Post, Jan 14 2013

This is to A220425 as 13 is to 2, to A220509 as 13 is to 3, to A220511 as 13 is to 5, to A220528 as 13 is to 7, and to A220653 as 13 is to 11. The subsequence of primes begins: 8387, 13065520903.

			a(2) = 2^13 + 13*2 + 13^2 = 8387.

G. C. Greubel, Table of n, a(n) for n = 0..895

Cf. A008455, A008593, A001020, A220425, A220509, A220511, A220528, A220653, A220787.

[n^13 + 13*n + 13^n: n in [0..30]]; // G. C. Greubel, Jan 05 2018

Table[n^13 + 13*n + 13^n, {n,0,30}] (* G. C. Greubel, Jan 05 2018 *)

makelist(n^13 + 13*n + 13^n,n,0,20); /* Martin Ettl, Jan 15 2013 */

for(n=0,30, print1(n^13 + 13*n + 13^n, ", ")) \\ G. C. Greubel, Jan 05 2018

A220701 Numbers k such that k^3 + 3*k + 3^k is prime.

Original entry on oeis.org

1, 2, 4, 5, 7, 17, 22, 47, 155, 167, 203, 277, 469, 629, 890, 1427, 4507, 5705, 6095, 9808, 10108, 12797, 16184, 31535, 33575

Offset: 1

Vincenzo Librandi, Jan 07 2013

a(26) > 10^5. - Michael S. Branicky, Oct 25 2024

Cf. A220509.

Select[Range[10000], PrimeQ[#^3 + 3*# + 3^#]&]

is(n)=ispseudoprime(n^3+3*n+3^n) \\ Charles R Greathouse IV, Jun 13 2017

a(21)-a(25) from Michael S. Branicky, Jul 13 2023

cp's OEIS Frontend

A220511 a(n) = n^5 + 5*n + 5^n.

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A220528 a(n) = n^7 + 7*n + 7^n.

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A220653 a(n) = n^11 + 11*n + 11^n.

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A182127 Main diagonal T(n,n) of array T(k,n) = n-th value of m^prime(k) + m*prime(k) + prime(k)^m.

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Maple

A209261 a(n) = n^13 + 13*n + 13^n.

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Magma

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Maxima

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A220701 Numbers k such that k^3 + 3*k + 3^k is prime.

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Mathematica

PARI

Extensions