A155211 -id:A155211 - cp's OEIS frontend

A152913 Primes of the form n^4 + (n+1)^4.

17, 97, 337, 881, 3697, 10657, 16561, 49297, 66977, 89041, 149057, 847601, 988417, 1146097, 1972097, 2522257, 2836961, 3553777, 3959297, 4398577, 5385761, 7166897, 11073217, 17653681, 32530177, 41532497, 44048497, 55272097, 61627201

Offset: 1

Vincenzo Librandi, Dec 15 2008

Also primes in A008514.

Sequence is disjoint to A005385: If n^4 + (n+1)^4 is a prime p, then (p-1)/2 = n^4 + 2*n^3 + 3*n^2 + 2*n. (p-1)/2 = 8 for n = 1 and (p-1)/2 is divisible by n for n > 1. In each case, (p-1)/2 is not prime.

			For n=3, n^4 + (n+1)^4 = 337 is prime and (337-1)/2 = 168 = 3*56 is not prime.

Vincenzo Librandi, Table of n, a(n) for n = 1..5000

Cf. A155211, A008514.

[ a: n in [1..80] | IsPrime(a) where a is n^4+(n+1)^4 ];

f[n_]:=n^4+(n+1)^4;lst={};Do[a=f[n];If[PrimeQ[a],AppendTo[lst,a]],{n,0,6!}];lst (* Vladimir Joseph Stephan Orlovsky, May 30 2009 *)
Select[Table[n^4+(n+1)^4,{n,0,700}],PrimeQ]
Select[Total/@Partition[Range[100]^4,2,1],PrimeQ] (* Harvey P. Dale, Sep 29 2023 *)

Edited and extended by Klaus Brockhaus, Dec 21 2008

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] &]

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] &];

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 *)

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, ", ")))

cp's OEIS Frontend

A152913 Primes of the form n^4 + (n+1)^4.

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

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

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

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

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

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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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Magma

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

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