A036097 Centered cube numbers: (n+1)^19+n^19.

1, 524289, 1162785755, 276040168411, 19348364235069, 628433226338621, 12008254925383639, 155514083261229015, 1494966905748847961, 11350851717672992089, 71159090448414546291, 380639089819037473139, 1781400289746069037525, 7438224249324360507861

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Never prime, as a(n) = (2n + 1) * (n^18 + 9n^17 + 81n^16 + 444n^15 + 1716n^14 + 4956n^13 + 11088n^12 + 19650n^11 + 27966n^10 + 32206n^9 + 30086n^8 + 22748n^7 + 13820n^6 + 6656n^5 + 2486n^4 + 695n^3 + 137n^2 + 17n + 1). Semiprime for n in {1, 3, 8, 39, 41, 54, 111, 119, 141 ...}. [Jonathan Vos Post, Aug 27 2011]

Sums of consecutive pairs of terms of A010807. - Wesley Ivan Hurt, Jul 13 2014

Examples

			1^19 + (1+1)^19 = 524289 = 3 * 174763, a semiprime.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral clusters, Inorgan. Chem. 24 (1985), 4545-4558.

Crossrefs

Cf. A010807, A036096, A036096.

Programs

Magma

[(n+1)^19+n^19: n in [0..20]]; // Vincenzo Librandi, Aug 28 2011

Maple

A036097:=n->(n+1)^19+n^19: seq(A036097(n), n=0..20); # Wesley Ivan Hurt, Jul 13 2014

Mathematica

Total/@Partition[Range[0,20]^19,2,1] (* Harvey P. Dale, Mar 04 2013 *)
f[n_] := n^19; Array[f[#] + f[# + 1] &, 14, 0] (* Robert G. Wilson v, Jul 22 2014 *)

Formula

a(n) = A010807(n+1) + A010807(n). - Wesley Ivan Hurt, Jul 13 2014