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A036097

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

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

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OFFSET

0,2

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

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.

FORMULA

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

EXAMPLE

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

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 *)