A027622 -id:A027622 - cp's OEIS frontend

A027620 a(n) = n + (n+1)^2 + (n+2)^3.

9, 32, 75, 144, 245, 384, 567, 800, 1089, 1440, 1859, 2352, 2925, 3584, 4335, 5184, 6137, 7200, 8379, 9680, 11109, 12672, 14375, 16224, 18225, 20384, 22707, 25200, 27869, 30720, 33759, 36992, 40425, 44064, 47915, 51984, 56277, 60800

Offset: 0

Patrick De Geest

Numbers n > 0 such that x^3 + 2*x^2 + n factors over the integers. - James R. Buddenhagen, Apr 19 2005

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Patrick De Geest, Palindromic Quasi_Under_Squares of the form n+(n+1)^2
Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
Milan Janjic and B. Petkovic, A Counting Function, arXiv 1301.4550 [math.CO], 2013.
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Cf. A000027, A027621, A027622, A028387.

[n + (n+1)^2 + (n+2)^3: n in [0..40]]; // Vincenzo Librandi, Aug 05 2011

[seq((n+3)^2*(n+1), n=0..40)]; # Zerinvary Lajos, Sep 24 2006

Table[n +(n+1)^2 +(n+2)^3, {n, 0, 40}] (* or *) LinearRecurrence[{4,-6,4,-1},{9,32,75,144}, 40] (* Harvey P. Dale, Feb 23 2021 *)

A027620(n):=n + (n+1)^2 + (n+2)^3$ makelist(A027620(n),n,0,15); /* Martin Ettl, Dec 13 2012 */

a(n)=n+(n+1)^2+(n+2)^3 \\ Charles R Greathouse IV, Oct 07 2015

[i+(i+1)^2+(i+2)^3 for i in range(0,38)] # Zerinvary Lajos, Jul 03 2008

a(n) = (n+1)*(n+3)^2. - Zerinvary Lajos, Sep 24 2006, corrected Dec 21 2010
G.f.: (9 - 4*x + x^2)/(1 - x)^4. - R. J. Mathar, Dec 21 2010
a(n) = coefficient of x^3 in the Maclaurin expansion of -1/((n+3)*x^2 + (n+3)*x + 1). - Francesco Daddi, Aug 04 2011
E.g.f.: (9 + 23*x + 10*x^2 + x^3)*exp(x). - G. C. Greubel, Aug 05 2022

A027621 a(n) = n + (n+1)^2 + (n+2)^3 + (n+3)^4.

Original entry on oeis.org

90, 288, 700, 1440, 2646, 4480, 7128, 10800, 15730, 22176, 30420, 40768, 53550, 69120, 87856, 110160, 136458, 167200, 202860, 243936, 290950, 344448, 405000, 473200, 549666, 635040, 729988, 835200, 951390, 1079296, 1219680

Offset: 0

Patrick De Geest

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Patrick De Geest, Palindromic Quasi_Under_Squares of the form n+(n+1)^2
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Cf. A000027, A027620, A027622, A028387.

[n + (n+1)^2 + (n+2)^3 + (n+3)^4: n in [0..40]]; // Vincenzo Librandi, Aug 05 2011

seq( (n+3)^2*(n^2 + 7*n + 10), n=0..40); # G. C. Greubel, Aug 05 2022

Table[Total[Table[(n+i)^(i+1),{i,0,3}]],{n,0,40}] (* or *) LinearRecurrence[ {5,-10,10,-5,1},{90,288,700,1440,2646},40] (* Harvey P. Dale, Jun 08 2017 *)

[i+(i+1)^2+(i+2)^3+(i+3)^4 for i in range(0,40)] # Zerinvary Lajos, Jul 03 2008

G.f.: 16/(1-x) + 16/(1-x)^2 + 16/(1-x)^3 + 18/(1-x)^4 + 24/(1-x)^5. - R. J. Mathar, Feb 22 2008
a(n) = (n+3)^2*(n^2 + 7*n + 10). - Bruno Berselli, Aug 05 2011
E.g.f.: (90 + 198*x + 107*x^2 + 19*x^3 + x^4)*exp(x). - G. C. Greubel, Aug 05 2022

A027830 Numbers k such that k + (k+1)^2 + (k+2)^3 + (k+3)^4 + (k+4)^5 is prime.

Original entry on oeis.org

1, 7, 11, 25, 35, 43, 45, 47, 51, 53, 57, 63, 65, 81, 91, 103, 113, 117, 121, 143, 149, 169, 173, 191, 193, 199, 201, 211, 213, 225, 235, 247, 253, 255, 263, 269, 299, 331, 333, 355, 357, 359, 373, 385, 387, 395, 399, 403, 411, 445, 453, 495, 519, 537, 579, 599

Offset: 1

Patrick De Geest

Numbers k such that A027622(k) is prime.

			k=1: k + (k+1)^2 + (k+2)^3 + (k+3)^4 + (k+4)^5 = 3413 = A027886(1),
k=7: k + (k+1)^2 + (k+2)^3 + (k+3)^4 + (k+4)^5 = 171851 = A027886(2),
k=11: k + (k+1)^2 + (k+2)^3 + (k+3)^4 + (k+4)^5 = 800143 = A027886(3).

P. De Geest, Palindromic Quasi_Under_Squares of the form n+(n+1)^2

Cf. A027622, A027886.

[n: n in [0..1000] |IsPrime(n+(n+1)^2+(n+2)^3+(n+3)^4+(n+4)^5)]; // Vincenzo Librandi, Nov 20 2010

With[{c=Total[Table[(#+i)^(i+1),{i,0,4}]]},Select[Range[600],PrimeQ[c]&]] (* Harvey P. Dale, May 07 2012 *)

is(n)=isprime(n+(n+1)^2+(n+2)^3+(n+3)^4+(n+4)^5) \\ Charles R Greathouse IV, Jun 13 2017

Edited by N. J. A. Sloane, May 21 2008 at the suggestion of R. J. Mathar

cp's OEIS Frontend

A027620 a(n) = n + (n+1)^2 + (n+2)^3.

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A027621 a(n) = n + (n+1)^2 + (n+2)^3 + (n+3)^4.

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A027830 Numbers k such that k + (k+1)^2 + (k+2)^3 + (k+3)^4 + (k+4)^5 is prime.

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