A154535 -id:A154535 - cp's OEIS frontend

A194185 Primes of the form k^16 + (k+1)^16.

65537, 4338014017, 2973697798081, 36054040477057, 314707907280257, 8746361693522261761, 4441930186581050471617, 1936348941361814438534657, 8260002645666200230661441, 157512780598351804823277697, 684655198104511486296198721, 21770695412796292350304592257

Offset: 1

Jonathan Vos Post, Aug 18 2011

Prime 16-dimensional centered cube numbers. This is to dimension 16 as A194155 is to dimension 8 and as A152913 is to dimension 4.

			a(1) = 1^16 + (1+1)^16 = 65537 = A100266(2).
a(2) = 3^16 + (3+1)^16 = 4338014017 = A100266(3).
a(3) = 5^16 + (5+1)^16 = 2973697798081 = A100266(4).
a(4) = 6^16 + (6+1)^16 = 36054040477057 = A100266(5).
a(5) = 7^16 + (7+1)^16 = 314707907280257 = A100266(6).
a(6) = 14^16 + (14+1)^16 = 8746361693522261761 = A100266(11).
a(7) = 21^16 + (21+1)^16 = 4441930186581050471617 = A100266(22).

Vincenzo Librandi, Table of n, a(n) for n = 1..3000

Cf. A000040, A154535, A100266, A152913, A194155.

[ a: n in [1..100] | IsPrime(a) where a is n^16+(n+1)^16 ]; // Vincenzo Librandi, Dec 07 2011

Select[Table[n^16+(n+1)^16,{n,0,800}],PrimeQ] (* Vincenzo Librandi, Dec 07 2011 *)
Select[Total/@Partition[Range[60]^16,2,1],PrimeQ] (* Harvey P. Dale, Dec 07 2017 *)

A155211 Numbers n such that n^4+(n+1)^4 is a prime.

Original entry on oeis.org

1, 2, 3, 4, 6, 8, 9, 12, 13, 14, 16, 25, 26, 27, 31, 33, 34, 36, 37, 38, 40, 43, 48, 54, 63, 67, 68, 72, 74, 78, 82, 87, 88, 89, 97, 98, 104, 105, 109, 110, 111, 119, 121, 122, 123, 129, 145, 156, 157, 162, 163, 166, 167, 172, 173, 179, 180, 182, 184, 186, 187, 189, 195

Offset: 1

Vincenzo Librandi, Jan 22 2009

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A153504, A154535.

[n: n in [1..200] |  IsPrime(n^4+(n+1)^4)]; // Vincenzo Librandi, Aug 31 2012

f[n_]:=n^4+(n+1)^4;lst={};Do[a=f[n];If[PrimeQ[a],AppendTo[lst,n]],{n,0,5!}];lst (* Vladimir Joseph Stephan Orlovsky, May 30 2009 *)
Select[Range[200],PrimeQ[#^4+(#+1)^4]&] (* Harvey P. Dale, Jun 15 2013 *)
Position[Total/@Partition[Range[200]^4,2,1],?PrimeQ]//Flatten (* _Harvey P. Dale, Sep 20 2023 *)

A194216 Primes of the form k^32 + (k+1)^32.

Original entry on oeis.org

3512911982806776822251393039617, 2211377674535255285545615254209921, 476961452964007550415682034114910337, 46677208572152524490331633250547044320123137

Offset: 1

Jonathan Vos Post, Aug 18 2011

Prime 32-dimensional centered cube numbers. This is to dimension 32 as A194185 is to dimension 16; as A194155 is to dimension 8; and as A152913 is to dimension 4.

			a(1) = 8^32 + (8 + 1)^32 = A100267(2).
a(2) = 10^32 + (10 + 1)^32 = A100267(3) = A176935(2).
a(3) = 12^32 + (12 + 1)^32 = A100267(4).
a(4) = 22^32 + (22 + 1)^32.

Vincenzo Librandi, Table of n, a(n) for n = 1..2000

Cf. A000040, A100267, A154535, A100266, A152913, A194155, A194185.

[a: n in [1..200] | IsPrime(a) where a is n^32+(n+1)^32]; // Vincenzo Librandi, Dec 08 2011

Select[Table[n^32+(n+1)^32,{n,1,3000}],PrimeQ] (* Vincenzo Librandi, Dec 08 2011 *)

A036085 Centered cube numbers: (n+1)^7 + n^7.

Original entry on oeis.org

1, 129, 2315, 18571, 94509, 358061, 1103479, 2920695, 6880121, 14782969, 29487171, 55318979, 98580325, 168162021, 276272879, 439294831, 678774129, 1022558705, 1506091771, 2173871739, 3081088541, 4295446429, 5899183335, 7991296871, 10689987049, 14135325801

Offset: 0

N. J. A. Sloane

Never prime, as a(n) = (2n+1)*(n^6 + 3n^5 + 9n^4 + 13n^3 + 11n^2 + 5n + 1). Semiprimes in the sequence begin for n = 1, 2, 8, 9, 21, 30, 33, 53, 65, 81, 83. - 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
Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Cf. A100267, A154535, A100266, A152913, A194155, A194185, A194216.

[(n+1)^7+n^7: n in [0..30]]; // Vincenzo Librandi, Aug 27 2011

a(n)=(n+1)^7+n^7 \\ Charles R Greathouse IV, Oct 07 2015

a(n) = A001015(n+1) + A001015(n).

G.f.: (1+x)*(x^6 + 120*x^5 + 1191*x^4 + 2416*x^3 + 1191*x^2 + 120*x + 1) / (x-1)^8. - R. J. Mathar, Aug 27 2011

A174156 Numbers n such that n^32+(n+1)^32 is a prime.

Original entry on oeis.org

8, 10, 12, 22, 100, 146, 154, 219, 246, 269, 287, 309, 336, 373, 392, 398, 423, 440, 449, 476, 515, 540, 557, 628, 671, 693, 715, 733, 746, 780, 848, 879, 913, 924, 926, 937, 974, 975, 1130, 1191, 1193, 1198, 1204, 1260, 1272, 1316, 1378, 1400, 1414, 1451

Offset: 1

Vincenzo Librandi, Mar 10 2010

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A153504, A154535, A155211.

[n: n in [1..1500] |  IsPrime(n^32+(n+1)^32 )];

lst={};Do[If[PrimeQ[n^32+(n+1)^32],AppendTo[lst,n]],{n,1500}];lst (* Vincenzo Librandi, Aug 31 2012 *)
Select[Range[1500], PrimeQ[#^32 + (# + 1)^32] &] (* Bruno Berselli, Aug 31 2012 *)
Position[Total/@Partition[Range[1460]^32,2,1],?(PrimeQ[#]&)]//Flatten (* _Harvey P. Dale, Jul 05 2021 *)

A174157 Numbers n such that n^64+(n+1)^64 is a prime.

Original entry on oeis.org

95, 302, 443, 546, 755, 850, 878, 962, 983, 988, 1014, 1026, 1349, 1433, 1541, 1711, 1735, 1897, 1901, 1958, 1961, 1966, 2052, 2058, 2070, 2096, 2142, 2167, 2170, 2208, 2333, 2421, 2471, 2490, 2503, 2527, 2571, 2637, 2643, 2813, 2820, 2885, 2994

Offset: 1

Vincenzo Librandi, Mar 10 2010

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Cf. A153504, A154535, A155211.

[n: n in [0..2000] | IsPrime(n^64+(n+1)^64)]

lst={}; Do[If[PrimeQ[n^64+(n+1)^64], AppendTo[lst, n]], {n, 3000}]; lst (* Vincenzo Librandi_, Aug 31 2012 *)
Position[Total/@Partition[Range[3000]^64,2,1],?(PrimeQ[#]&)]//Flatten (* _Harvey P. Dale, Aug 01 2021 *)

A215431 Numbers n such that n^128+(n+1)^128 is a prime.

Original entry on oeis.org

31, 37, 65, 191, 255, 287, 359, 786, 836, 1178, 1229, 1503, 1601, 1609, 2093, 2103, 2254, 2307, 2471, 2934, 2978, 3215, 3220, 3363, 3402, 3705, 3724, 3892, 3894, 3976, 4094, 4478, 4490, 4535, 4566, 4683, 4749, 4752, 4789, 4918, 5064, 6061, 6162, 6167

Offset: 1

Vincenzo Librandi, Aug 31 2012

Vincenzo Librandi, Table of n, a(n) for n = 1..250

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

Select[Range[7000], PrimeQ[#^128 + (# + 1)^128] &]

A036087 Centered cube numbers: a(n) = (n+1)^9 + n^9.

Original entry on oeis.org

1, 513, 20195, 281827, 2215269, 12030821, 50431303, 174571335, 521638217, 1387420489, 3357947691, 7517728043, 15764279725, 31265546157, 59104406159, 107162836111, 187307353233, 316947166865

Offset: 0

N. J. A. Sloane

Never prime nor semiprime, as a(n) = (2n+1) * (n^2 + n + 1) * (n^6 + 3n^5 + 12n^4 + 19n^3 + 15n^2 + 6n + 1). - Jonathan Vos Post, Aug 26 2011

Triprimes (A014612) if n = 2, 5, 6, 14, 21, 75, 90, ... - R. J. Mathar, 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
Index entries for linear recurrences with constant coefficients, signature (10, -45, 120, -210, 252, -210, 120, -45, 10, -1).

Cf. A036085, A100267, A154535, A100266, A152913, A194155, A194185, A194216.

[(n+1)^9+n^9: n in [0..20]]; // Vincenzo Librandi, Aug 27 2011

Total/@Partition[Range[0,20]^9,2,1] (* Harvey P. Dale, Jan 31 2015 *)
LinearRecurrence[{10,-45,120,-210,252,-210,120,-45,10,-1},{1,513,20195,281827,2215269,12030821,50431303,174571335,521638217,1387420489},20] (* Harvey P. Dale, Jan 21 2023 *)

a(n)=(n+1)^9+n^9 \\ Charles R Greathouse IV, Jan 31 2017

a(n) = A001017(n+1) + A001017(n).

G.f.: (1+x)*(x^8 + 502*x^7 + 14608*x^6 + 88234*x^5 + 156190*x^4 + 88234*x^3 + 14608*x^2 + 502*x + 1) / (x-1)^10. - R. J. Mathar, Aug 27 2011

A036088 Centered cube numbers: (n+1)^10 + n^10.

Original entry on oeis.org

1, 1025, 60073, 1107625, 10814201, 70231801, 342941425, 1356217073, 4560526225, 13486784401, 35937424601, 87854788825, 199775856073, 427113146825, 865905045601, 1676162018401, 3115505528225

Offset: 0

N. J. A. Sloane

Never prime, as a(n) = (2n^2 + 2n + 1) * (n^8 + 4n^7 + 18n^6 + 40n^5 + 56n^4 + 50n^3 + 27n^2 + 8n + 1), multiple of A001844(n). Semiprime for n in {2, 4, 7, 14, 19, 22, 32, 60, 65, 70, 87, 99, 102, 135, 137, ...}. - 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. A036085, A036087, A100267, A154535, A100266, A152913, A194155, A194185, A194216.

[(n+1)^10+n^10: n in [0..20]]; // Vincenzo Librandi, Aug 27 2011

Total/@Partition[Range[0,20]^10,2,1] (* Harvey P. Dale, Aug 04 2019 *)

G.f.: -(x^8 + 1012*x^7 + 46828*x^6 + 408364*x^5 + 901990*x^4 + 408364*x^3 + 46828*x^2 + 1012*x + 1)*(1+x)^2 / (x-1)^11. - R. J. Mathar, Aug 27 2011

A215432 Numbers n such that n^256+(n+1)^256 is a prime.

Original entry on oeis.org

85, 86, 157, 190, 195, 421, 504, 539, 621, 895, 1018, 1159, 1314, 1463, 1482, 1538, 1959, 2036, 2368, 2537, 2618, 2651, 3085, 3148, 3205, 3230, 3347, 3370, 3807, 4061, 4089, 4448, 4641, 4697, 4723, 4851, 4945

Offset: 1

Vincenzo Librandi, Aug 31 2012

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

Select[Range[5000], PrimeQ[#^256 + (# + 1)^256] &];

cp's OEIS Frontend

A194185 Primes of the form k^16 + (k+1)^16.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Mathematica

A155211 Numbers n such that n^4+(n+1)^4 is a prime.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

A194216 Primes of the form k^32 + (k+1)^32.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Mathematica

A036085 Centered cube numbers: (n+1)^7 + n^7.

Views

Author

Keywords

Comments

References

Links

Crossrefs

Programs

Magma

PARI

Formula

A174156 Numbers n such that n^32+(n+1)^32 is a prime.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

A174157 Numbers n such that n^64+(n+1)^64 is a prime.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

A215431 Numbers n such that n^128+(n+1)^128 is a prime.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

A036087 Centered cube numbers: a(n) = (n+1)^9 + n^9.

Views

Author

Keywords

Comments

References

Links

Crossrefs

Programs

Magma