A153504 -id:A153504 - cp's OEIS frontend

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

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, ", ")))

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

A168149 Numbers n such that n^8+(n-1)^8 is a prime.

Original entry on oeis.org

2, 6, 18, 24, 33, 34, 36, 40, 43, 67, 69, 77, 79, 91, 114, 119, 130, 153, 182, 187, 189, 199, 221, 222, 230, 232, 288, 301, 307, 308, 312, 317, 349, 363, 381, 402, 410, 415, 427, 444, 454, 465, 488, 504, 509, 511, 512, 561, 573, 594, 629, 645, 647, 663, 692

Offset: 1

Vincenzo Librandi, Nov 19 2009

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

Cf. A153504.

[n: n in [0..700] | IsPrime(n^8 + (n-1)^8)]; // Vincenzo Librandi, Apr 05 2013

Select[Range[0, 1000], PrimeQ[#^8 + (#-1)^8]&] (* Vincenzo Librandi, Apr 05 2013 *)

308 and 512 inserted by R. J. Mathar, Nov 19 2009

A244932 Least number k > n such that k^8 + n^8 is prime.

Original entry on oeis.org

2, 13, 10, 17, 6, 37, 12, 13, 16, 27, 24, 71, 16, 31, 64, 43, 18, 43, 26, 23, 32, 29, 24, 79, 32, 53, 34, 61, 92, 47, 40, 33, 34, 57, 36, 47, 40, 53, 40, 79, 44, 43, 68, 91, 68, 57, 66, 61, 60, 53, 58, 83, 60, 91, 94, 61, 82, 61, 70, 101, 82, 71, 68, 145, 82, 67, 76, 69, 100

Offset: 1

Derek Orr, Jul 08 2014

nonn

a(n) = n+1 iff n is in A153504.

			13^8 + 14^8 = 2291519777 is not prime, 13^8 + 15^8 = 3378621346 is not prime. 13^8 + 16^8 = 5110698017 is prime. Thus a(13) = 16.

Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

Cf. A158979, A089489, A242553.

a(n)=for(k=n+1,10^4,if(isprime(k^8+n^8),return(k)))
n=1;while(n<100,print1(a(n),", ");n++)

import sympy
from sympy import isprime
def a(n):
  for k in range(n+1,10**4):
    if isprime(k**8+n**8):
      return k
n = 1
while n < 100:
  print(a(n),end=', ')
  n += 1

cp's OEIS Frontend

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

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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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A168149 Numbers n such that n^8+(n-1)^8 is a prime.

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Mathematica

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A244932 Least number k > n such that k^8 + n^8 is prime.

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