A239787 -id:A239787 - cp's OEIS frontend

A240235 Least number k such that k*n^k - 1 is prime. a(n) = 0 if no such number exists.

3, 2, 1, 1, 8, 1, 2, 1, 10, 2, 2, 1, 2, 1, 2, 167, 2, 1, 12, 1, 2, 2, 29028, 1, 2, 3, 10, 2, 26850, 1, 8, 1, 42, 2, 6, 2, 24, 1, 2, 3, 2, 1, 2, 1, 2, 2, 140, 1, 2, 2, 22, 2, 8, 1, 2064, 2, 468, 6, 2, 1, 362, 1, 2, 2, 6, 3, 26, 1, 2, 3, 20, 1, 2, 1, 28, 2, 38, 5, 3024, 1, 2, 81, 858, 1

Offset: 1

Derek Orr, Apr 02 2014

nonn

a(n) = 1 iff n-1 is prime.

a(145) is either 0 or > 275000. - Robert G. Wilson v, Jan 23 2017

			1*1^1 - 1 = 0 is not prime. 2*1^2 - 1 = 1 is not prime. 3*1^3 - 1 = 2 is prime. Thus, a(1) = 3.

Robert G. Wilson v, Table of n, a(n) for n = 1..144
Steven Harvey, Generalized Woodall Primes

Cf. A066049, A239787, A281141.

a(n)=k=1;while(!ispseudoprime(k*n^k-1),k++);return(k); n=1;while(n<100,print(a(n));n+=1)

a(23) and a(29) given using link. - Derek Orr, Aug 16 2014

A239938 a(n) = least number k > 0 such that n*k^n - 1 is prime, or 0 if no such k exists.

Original entry on oeis.org

3, 2, 1, 1, 4, 1, 8, 1, 40, 3, 10, 1, 56, 1, 10, 0, 46, 1, 6, 1, 42, 51, 4, 1, 8, 67, 0, 18, 102, 1, 98, 1, 38, 6, 136, 0, 90, 1, 10, 3, 52, 1, 12, 1, 18, 3, 28, 1, 72, 165, 40, 657, 418, 1, 44, 205, 94, 9, 426, 1, 482, 1, 4, 0, 418, 252, 38, 1, 400, 165, 28, 1, 140

Offset: 1

Derek Orr, Mar 29 2014

nonn

a(n) = 1 iff n-1 is prime.
If a(n) = 0 then n is in A097764. Note the converse is not true: a(4) = 1, not 0.
Up to a(1000), the largest term is a(456) = 947310. The PFGW program has been used to certify all the terms up to a(1000), using the 'N+1' deterministic test. - Giovanni Resta, Mar 30 2014

			1*1^1 - 1 = 0 is not prime. 1*2^1 - 1 = 1 is not prime. 1*3^1 - 1 = 2 is prime. Thus a(1) = 3.

Giovanni Resta, Table of n, a(n) for n = 1..1000

Cf. A066049, A097764, A239787.

nope[n_] := n > 4 && Catch@Block[{p = 2}, While[n >= p^p, If[ IntegerQ[ n^(1/p)/p], Throw@ True]; p = NextPrime@ p]; False]; a[n_] := If[nope@ n, 0, Block[{k = 1}, While[! PrimeQ[n*k^n - 1], k++]; k]]; Array[a, 80] (* Giovanni Resta, Mar 30 2014 *)
A239938[n_] := If[n != 4 && # != 1 && GCD[n, #] != 1 &[GCD @@ FactorInteger[n][[All, -1]]], 0, NestWhile[# + 1 &, 1, Not@PrimeQ[n #^n - 1] &]]; Array[A239938, 73] (* JungHwan Min, Dec 28 2015 *)

Pro(n) = for(k=1,10^4,if(ispseudoprime(n*k^n-1),return(k)));
n=1; while(n<100,print1(Pro(n), ", ");n+=1)

A239788 Numbers n such that 3n^3 +/- 1 are twin primes.

Original entry on oeis.org

4, 10, 14, 36, 54, 64, 70, 86, 150, 174, 176, 180, 200, 306, 384, 440, 494, 650, 706, 800, 824, 924, 976, 980, 986, 1020, 1026, 1054, 1360, 1464, 1504, 1506, 1536, 1564, 1604, 1680, 1724, 1736, 2066, 2076, 2116, 2134, 2136, 2166, 2200, 2220, 2314, 2380, 2456

Offset: 1

Derek Orr, Mar 26 2014

Numbers in this sequence are all even.

			3*4^3-1 = 191 is prime and 3*4^3+1 = 193 is prime. Thus, 4 is a member of this sequence.

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

Cf. A116954, A239787.

[n: n in [0..5000] | IsPrime(3*n^3-1) and IsPrime(3*n^3+1)]; // Vincenzo Librandi, Mar 29 2014

Select[Range[5000], PrimeQ[3 #^3 - 1] && PrimeQ[3 #^3 + 1]&] (* Vincenzo Librandi, Mar 29 2014 *)

s=[]; for(n=1, 3000, if(isprime(3*n^3-1) && isprime(3*n^3+1), s=concat(s, n))); s \\ Colin Barker, Mar 27 2014

import sympy
from sympy import isprime
{print(n) for n in range(10**4) if isprime(3*(n**3)+1) and isprime(3*(n**3)-1)}

cp's OEIS Frontend

A240235 Least number k such that k*n^k - 1 is prime. a(n) = 0 if no such number exists.

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A239938 a(n) = least number k > 0 such that n*k^n - 1 is prime, or 0 if no such k exists.

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A239788 Numbers n such that 3n^3 +/- 1 are twin primes.

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Python