A238847 -id:A238847 - cp's OEIS frontend

A270927 Smallest k such that k*n^m + 1 is prime, case m=4.

1, 1, 2, 1, 18, 1, 6, 3, 6, 7, 46, 5, 10, 3, 8, 1, 16, 2, 28, 1, 2, 7, 16, 1, 24, 12, 10, 1, 10, 2, 6, 7, 26, 1, 12, 3, 6, 3, 8, 16, 10, 3, 22, 16, 2, 1, 6, 1, 36, 3, 6, 3, 16, 1, 18, 1, 8, 12, 16, 10, 12, 31, 2, 10, 22, 2, 36, 21, 40, 6, 12, 18, 6, 1, 6, 7, 10, 2, 18, 1, 2, 1, 22, 2, 12, 18, 6, 1, 18, 1, 58, 3, 12, 7, 24, 2, 16, 3, 16, 6, 6, 7, 46, 25, 2, 1, 12, 7, 18, 12, 46, 3, 12, 5, 10, 3, 48, 1, 16, 2

Offset: 1

Zak Seidov, Mar 26 2016

nonn

Zak Seidov, Table of n, a(n) for n = 1..10000
Zak Seidov,20 related sequences.

Cf. A034693 (m=1), A035092 (m=2), A238847 (m=3).

With[{m = 4, nn = 120}, Table[SelectFirst[Range@ nn, PrimeQ[# n^m + 1] &], {n, nn}]] (* Michael De Vlieger, Mar 26 2016, Version 10 *)
sk[n_]:=Module[{k=1,c=n^4},While[!PrimeQ[k*c+1],k++];k]; Array[sk,120] (* Harvey P. Dale, Jun 05 2021 *)

{m=4;for(n=1,10000,k=1;while(!isprime(k*n^m+1),k++);
write("b270927.txt",n" "k))} \\ for b-file - Zak Seidov, Mar 26 2016

A239021 Smallest number k such that kn +/- 1, kn^2 +/- 1, and k*n^3 +/- 1 are three sets of twin primes. a(n) = 0 if no such number exists.

Original entry on oeis.org

4, 105525, 10990, 15855, 344190, 2, 74580, 11580, 165592, 3759, 204918, 12670, 99090, 78, 3978, 11655, 8979180, 10605, 55188, 1221, 2, 23340, 4431420, 39158, 58464, 87318, 45420, 15780, 210, 91, 289422, 19740, 186410, 1293, 137664, 747, 443730, 94920, 278278

Offset: 1

Derek Orr, Mar 09 2014

nonn

			1*6 +/- 1 (5 and 7), 1*6^2 +/- 1 (35 and 37), and 1*6^3 +/- 1 (215 and 217) are not three sets of twin primes. However, 2*6 +/- 1 (11 and 13), 2*6^2 +/- 1 (71 and 73), and 2*6^3 +/- 1 (431 and 433) are three sets of twin primes. Thus, a(6) = 2.

Cf. A238847, A238848, A231819, A053989, A035092, A034693.

from sympy import isprime
def b(n):
  for k in range(10**8):
    if isprime(k*n+1) and isprime(k*n-1) and isprime(k*(n**2)+1) and isprime(k*(n**2)-1) and isprime(k*(n**3)+1) and isprime(k*(n**3)-1):
      return k
n = 1
while n < 100:
  print(b(n))
  n += 1

cp's OEIS Frontend

A270927 Smallest k such that k*n^m + 1 is prime, case m=4.

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A239021 Smallest number k such that kn +/- 1, kn^2 +/- 1, and k*n^3 +/- 1 are three sets of twin primes. a(n) = 0 if no such number exists.

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Python

cp's OEIS Frontend

A270927 Smallest k such that k*n^m + 1 is prime, case m=4.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

A239021 Smallest number k such that k*n +/- 1, k*n^2 +/- 1, and k*n^3 +/- 1 are three sets of twin primes. a(n) = 0 if no such number exists.

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Author

Keywords

Examples

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Python

A239021 Smallest number k such that kn +/- 1, kn^2 +/- 1, and k*n^3 +/- 1 are three sets of twin primes. a(n) = 0 if no such number exists.