A154535 -id:A154535 - cp's OEIS frontend

A036089 Centered cube numbers: (n+1)^11 + n^11.

1, 2049, 179195, 4371451, 53022429, 411625181, 2340123799, 10567261335, 39970994201, 131381059609, 385311670611, 1028320041299, 2535168764725, 5841725563701, 12699321029039, 26241941903791, 51864082352049

Offset: 0

N. J. A. Sloane

Never prime, as a(n) = (2*n+1) * (n^10 + 5*n^9 + 25*n^8 + 70*n^7 + 130*n^6 + 166*n^5 + 148*n^4 + 91*n^3 + 37*n^2 + 9*n + 1). - 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 (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).

Cf. A008455, A036087, A036088, A100267, A154535, A100266, A152913, A194155, A194185, A194216.

[(n+1)^11+n^11: n in [0..20]]; // Vincenzo Librandi, Aug 27 2011

Vec((1 + x)*(1 + 2036*x + 152637*x^2 + 2203488*x^3 + 9738114*x^4 + 15724248*x^5 + 9738114*x^6 + 2203488*x^7 + 152637*x^8 + 2036*x^9 + x^10) / (1 - x)^12 + O(x^40)) \\ Colin Barker, Feb 06 2020

From Colin Barker, Feb 06 2020: (Start)
G.f.: (1 + x)*(1 + 2036*x + 152637*x^2 + 2203488*x^3 + 9738114*x^4 + 15724248*x^5 + 9738114*x^6 + 2203488*x^7 + 152637*x^8 + 2036*x^9 + x^10) / (1 - x)^12.
a(n) = 12*a(n-1) - 66*a(n-2) + 220*a(n-3) - 495*a(n-4) + 792*a(n-5) - 924*a(n-6) + 792*a(n-7) - 495*a(n-8) + 220*a(n-9) - 66*a(n-10) + 12*a(n-11) - a(n-12) for n>11.
(End)

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

Original entry on oeis.org

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

A215433 Numbers n such that n^512 + (n+1)^512 is a prime.

Original entry on oeis.org

59, 864, 1455, 1723, 2118, 2172, 2460, 2851, 2916, 2971, 3193, 3476, 3747, 3782, 3795

Offset: 1

Vincenzo Librandi, Aug 31 2012

Cf. A027861, A153504, A154535, A155211, A174156, A174157, A215431, A215432.

Select[Range[0, 4000], PrimeQ[#^512 + (# + 1)^512] &]
Position[Partition[Range[3800]^512,2,1],?(PrimeQ[Total[#]]&)]//Flatten (* _Harvey P. Dale, Aug 03 2024 *)

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 *)

A274234 Numbers n such that n^1024 + (n+1)^1024 is prime.

Original entry on oeis.org

1078, 2020, 2471, 3255, 4200, 5135, 5185, 6218, 6823, 7220, 8416, 9003, 9008, 9267, 9396, 9689, 10316, 11150, 11250, 11543, 11652, 12960, 14021, 14201, 16523, 16751, 17006, 17054, 17747, 17874, 18157, 18640, 18834, 20478, 20481, 20794, 21147, 22166, 22608, 22638, 24450, 24677, 24894, 25709

Offset: 1

Tim Johannes Ohrtmann, Jun 15 2016

nonn

The first five terms are certified primes, according to: factordb/certoverview.php. The others are probable primes. - Lewis Baxter, Jan 05 2021

Richard Fischer, Primzahlen mit der Form (B+1)^N+B^N.
Henri Lifchitz & Renaud Lifchitz, Search for : x^1024+y^1024.

Cf. A005097, A027861, A155211, A153504, A154535, A174156, A174157, A215431, A215432, A215433, A274235, A274236, A274237.

[n: n in [1..10000] |IsPrime(n^1024 + (n+1)^1024)]

Select[Range[1, 10000], PrimeQ[#^1024 + (#+1)^1024] &]

for(n=1, 10000, if(isprime(n^1024 + (n+1)^1024), print1(n, ", ")))

A274235 Numbers n such that n^2048 + (n+1)^2048 is prime.

Original entry on oeis.org

754, 1289, 1368, 1813, 3159, 3280, 3301, 4976, 6204, 6283, 6723, 6904, 7141, 10246, 11417, 13268, 15456, 19428, 19683, 19698, 20298, 21484, 22543, 23702, 23815, 24747, 27010, 32319, 34133, 36201, 37030, 39438, 41292, 44472, 47623, 50198, 51031, 51370, 51521, 52628, 53073, 53309, 53767, 55911, 56630, 59424

Offset: 1

Tim Johannes Ohrtmann, Jun 15 2016

nonn

The terms correspond only to probable primes.

Richard Fischer, Primzahlen mit der Form (B+1)^N+B^N.
Henri Lifchitz & Renaud Lifchitz, Search for : x^2048+y^2048.

Cf. A005097, A027861, A155211, A153504, A154535, A174156, A174157, A215431, A215432, A215433, A274234, A274236, A274237.

[n: n in [1..10000] |IsPrime(n^2048 + (n+1)^2048)];

Select[Range[1, 10000], PrimeQ[#^2048 + (#+1)^2048] &]

for(n=1, 10000, if(isprime(n^2048 + (n+1)^2048), print1(n, ", ")))

A274236 Numbers k such that k^4096 + (k+1)^4096 is prime.

Original entry on oeis.org

311, 2741, 3582, 5293, 6289, 12080, 14082, 16886, 17971, 19936, 21454, 21486, 26652, 26904, 28314, 34693, 35778, 36292, 40868, 43819, 46356, 46467, 49653, 53996, 57150, 58169, 64937, 67398, 77383, 82577, 86031, 86102, 87352, 87684, 89030, 93340, 95346, 97320, 98191, 111483, 113947, 118052, 125442, 125836, 126157, 127832, 130794

Offset: 1

Tim Johannes Ohrtmann, Jun 15 2016

nonn

The terms correspond only to probable primes.

Richard Fischer, Primzahlen mit der Form (B+1)^N+B^N.
Henri Lifchitz and Renaud Lifchitz, Search for : x^4096+y^4096.

Cf. A005097, A027861, A155211, A153504, A154535, A174156, A174157, A215431, A215432, A215433, A274234, A274235, A274237.

[n: n in [1..10000] |IsPrime(n^4096 + (n+1)^4096)];

Select[Range[1, 10000], PrimeQ[#^4096 + (#+1)^4096] &]

for(n=1, 10000, if(isprime(n^4096 + (n+1)^4096), print1(n, ", ")))

A274237 Numbers k such that k^8192 + (k+1)^8192 is prime.

Original entry on oeis.org

3508, 5209, 13428, 15347, 16339, 17779, 22548, 37726, 40408

Offset: 1

Tim Johannes Ohrtmann, Jun 15 2016

The terms correspond only to probable primes.

Richard Fischer, Primzahlen mit der Form (B+1)^N+B^N.
Henri Lifchitz and Renaud Lifchitz, Search for: x^8192+y^8192.

Cf. A005097, A027861, A155211, A153504, A154535, A174156, A174157, A215431, A215432, A215433, A274234, A274235, A274236.

[n: n in [1..10000] |IsPrime(n^8192 + (n+1)^8192)]

Select[Range[1, 10000], PrimeQ[#^8192 + (#+1)^8192] &]

for(n=1, 10000, if(isprime(n^8192 + (n+1)^8192), print1(n, ", ")))

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

cp's OEIS Frontend

A036089 Centered cube numbers: (n+1)^11 + n^11.

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

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A215433 Numbers n such that n^512 + (n+1)^512 is a prime.

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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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A274234 Numbers n such that n^1024 + (n+1)^1024 is prime.

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A274235 Numbers n such that n^2048 + (n+1)^2048 is prime.

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A274236 Numbers k such that k^4096 + (k+1)^4096 is prime.

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