A152913 -id:A152913 - cp's OEIS frontend

A036090 Centered cube numbers: (n+1)^12 + n^12.

1, 4097, 535537, 17308657, 260917841, 2420922961, 16018069537, 82560763937, 351149013217, 1282429536481, 4138428376721, 12054528824977, 32214185570737, 79991997497777, 186440250265921, 411221314601281

Offset: 0

N. J. A. Sloane

nonn

Never prime, as a(n) = (2n^4 + 4n^3 + 6n^2 + 4n + 1) * (n^8 + 4n^7 + 22n^6 + 52n^5 + 69n^4 + 56n^3 + 28n^2 + 8n + 1) Semiprime for n in {1, 2, 3, 6, 14, 16, 36, 87, 97, 109, 110, 119, 121, 163, 195, ...}. - Jonathan Vos Post, Aug 26 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. A008456, A036088, A036089, A100267, A154535, A100266, A152913, A194155, A194185, A194216.

[(n+1)^12+n^12: n in [0..20]]; // Vincenzo Librandi, Aug 27 2011

Total/@Partition[Range[0,20]^12,2,1] (* Harvey P. Dale, May 09 2018 *)

G.f.: -(x^10 + 4082*x^9 + 474189*x^8 + 9713496*x^7 + 56604978*x^6 + 105907308*x^5 + 56604978*x^4 + 9713496*x^3 + 474189*x^2 + 4082*x + 1)*(1+x)^2 / (x-1)^13. - R. J. Mathar, Aug 27 2011

A036092 Centered cube numbers: a(n) = (n+1)^14 + n^14.

Original entry on oeis.org

1, 16385, 4799353, 273218425, 6371951081, 84467679721, 756587236945, 5076269583953, 27274838966065, 122876792454961, 479749833583241, 1663668298132105, 5221294850248153, 15049383211257305, 40304932850948641, 101250520063318561, 240435420597328865

Offset: 0

N. J. A. Sloane

Never prime, as a(n) = (2n^2 + 2n + 1) * (n^12 + 6n^11 + 39n^10 + 140n^9 + 341n^8 + 590n^7 + 741n^6 + 680n^5 + 451n^4 + 210n^3 + 65n^2 + 12n + 1). Semiprime for n in {2, 5, 22, 24, 34, 35, 39, 84, 217, 220, 285, ...}. - Jonathan Vos Post, Aug 26 2011

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.
Index entries for linear recurrences with constant coefficients, signature (15,-105,455,-1365,3003,-5005,6435,-6435,5005,-3003,1365,-455,105,-15,1).

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

[(n+1)^14+n^14: n in [0..20]]; // Vincenzo Librandi, Aug 27 2011

G.f.: -(x +1)^2*(x^12 +16368*x^11 +4520946*x^10 +193889840*x^9 +2377852335*x^8 +10465410528*x^7 +17505765564*x^6 +10465410528*x^5 +2377852335*x^4 +193889840*x^3 +4520946*x^2 +16368*x +1) / (x -1)^15. - Colin Barker, Feb 16 2015

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

Original entry on oeis.org

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

A122902 First occurrence of exponent n in A080121 corresponding to the minimum prime of the form (k^(2^n) + (k+1)^(2^n)) = A122900(k).

Original entry on oeis.org

1, 3, 23, 21, 10, 95, 255, 86, 59

Offset: 1

Alexander Adamchuk, Sep 18 2006, Oct 01 2006

Minimum primes of the form n^(2^m) + (n+1)^(2^m) are listed in A122900. The exponents m are listed in A080121.

a(10)-a(13)>1000, a(14)-a(16)>100.

			A080121 begins with 1,1,2,1,1,2,1,2,1,5,?,1,2,1,?,2,1,?,1,?,4,1,3,1,..., where the unknown terms (denoted with ?) are at least 10. So a(1) = 1, a(2) = 3, a(3) = 23, a(4) = 21, a(5) = 10.

T. D. Noe, Table of generalized Fermat primes of the form (k+1)^2^m + k^2^m
Eric Weisstein's World of Mathematics, Generalized Fermat Number

Cf. A077659, A080121, A122900, A080208, A078902, A080134, A019434, A153504, A152913, A194185.

Edited by Max Alekseyev, Sep 09 2020

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.

cp's OEIS Frontend

A036090 Centered cube numbers: (n+1)^12 + n^12.

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A036092 Centered cube numbers: a(n) = (n+1)^14 + n^14.

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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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A122902 First occurrence of exponent n in A080121 corresponding to the minimum prime of the form (k^(2^n) + (k+1)^(2^n)) = A122900(k).

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

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