A100266 -id:A100266 - cp's OEIS frontend

A194553 Centered cube numbers: (n+1)^25 + n^25.

1, 33554433, 847322163875, 1126747195452067, 299149123783795749, 28728311253806654501, 1369498907693894602183, 39120000482621126610375, 755676919554809750479817, 10717897987691852588770249, 118347059433883722041830251

Offset: 0

Jonathan Vos Post, Aug 28 2011

Can never be prime as a(n) = (2*n+1) * (n^4 + 2*n^3 + 4*n^2 + 3*n+1) * (n^20 + 10*n^19 + 120*n^18 + 795*n^17 + 3685*n^16 + 12752*n^15 + 33965*n^14 + 71205*n^13 + 119580*n^12 + 162965*n^11 + 181754*n^10 + 166595*n^9 + 125515*n^8 +77415*n^7 + 38745*n^6 + 15503*n^5 + 4845*n^4 + 1140*n^3 + 190*n^2 + 20*n + 1).

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (26, -325, 2600, -14950, 65780, -230230, 657800, -1562275, 3124550, -5311735, 7726160, -9657700, 10400600, -9657700, 7726160, -5311735, 3124550, -1562275, 657800, -230230, 65780, -14950, 2600, -325, 26, -1).

Cf. A000040, A036085-A036102, A100267, A154535, A100266, A152913, A194155, A194185, A194216.

[(n+1)^25+n^25: n in [0..10]]; // Vincenzo Librandi, Sep 21 2011

Total/@Partition[Range[0,20]^25,2,1] (* Harvey P. Dale, Dec 03 2015 *)

A036095 Centered cube numbers: a(n) = (n+1)^17 + n^17.

Original entry on oeis.org

1, 131073, 129271235, 17309009347, 780119322309, 17689598897861, 249557173431943, 2484430327672455, 18928981513351817, 116677181699666569, 605447028499293771, 2724058135239730763, 10869027026121774925

Offset: 0

N. J. A. Sloane

Never prime, as a(n) = (2n + 1) * (n^16 + 8n^15 + 64n^14 + 308n^13 + 1036n^12 + 2576n^11 + 4900n^10 + 7274n^9 + 8518n^8 + 7896n^7 + 5776n^6 + 3300n^5 + 1444n^4 + 468n^3 + 106n^2 + 15n + 1). Semiprime for n in {1, 5, 21, 29, 33, ...}. - Jonathan Vos Post, Aug 27 2011

B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral clusters, Inorgan. Chem. 24 (1985), 4545-4558.

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Cf. A000040, A036085, A036087, A036088, A036089, A036090, A036091, A036092, A036093, A100267, A154535, A100266, A152913, A194155, A194185, A194216.

[(n+1)^17+n^17: n in [0..20]]; // Vincenzo Librandi, Aug 28 2011

A194566 Centered cube numbers: (n+1)^100+n^100.

Original entry on oeis.org

1, 1267650600228229401496703205377, 515377520732011332304111729993850674198810727377, 1606938044259505653062694103672199063651968615055494942823377

Offset: 0

Jonathan Vos Post, Aug 29 2011

Can never be prime, and after a(0) must have at least 3 prime factors, as a(n) = (2*n^4 + 4*n^3 + 6*n^2 + 4*n + 1) * p_16(n) * p_80(n).

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Cf. A036085-A036102, A100267, A154535, A100266, A152913, A194155, A194185, A194216, A194553.

a:= n-> (n+1)^100 +n^100: seq (a(n), n=0..20);

Total/@Partition[Range[0,5]^100,2,1] (* Harvey P. Dale, Aug 10 2013 *)

a(n) = (n+1)^100 + n^100.

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A194553 Centered cube numbers: (n+1)^25 + n^25.

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A036095 Centered cube numbers: a(n) = (n+1)^17 + n^17.

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A194566 Centered cube numbers: (n+1)^100+n^100.

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