A138066 -id:A138066 - cp's OEIS frontend

A255707 Least number k > 0 such that (2*n-1)^k - 2 is prime, or 0 if no such number exists.

0, 2, 1, 1, 1, 4, 1, 1, 6, 1, 1, 24, 1, 2, 2, 1, 1, 2, 2, 1, 4, 1, 1, 2, 1, 8, 4, 1, 12, 4, 1, 1, 8, 3, 1, 2, 1, 1, 2, 38, 1, 4, 1, 4, 2, 1, 2, 4, 747, 1, 4, 1, 1, 2, 1, 1, 10, 1, 2, 2, 2, 6, 42, 2, 1, 2, 1, 2, 10, 1, 1, 4, 2, 16, 50, 1, 1, 2, 22, 1, 2, 38

Offset: 1

Robert Price, Mar 02 2015

nonn

Michel Marcus, Table of n, a(n) for n = 1..152 (terms 1..143 from Robert Price)
Carlos Rivera, Puzzle 887. p(n)^c-2 is prime, The Prime Puzzles and Problems Connection.

Cf. A079706, A084712, A084713, A084714, A098090, A138066.

lst = {0}; For[n = 2, n ≤ 143, n++, For[k = 1, k >= 1, k++, If[PrimeQ[(2*n - 1)^k - 2], AppendTo[lst, k]; Break[]]]]; lst

a(n)=if(n==1,return(0));k=1;while(k,if(ispseudoprime((2*n-1)^k-2),return(k));k++)
vector(50,n,a(n)) \\ Derek Orr, Mar 03 2015

a(A098090(n)) = 1. - Michel Marcus, Mar 03 2015

A250200 Least number k>1 such that (2n-1)^k - 2 is prime, or 0 if no such number exists.

Original entry on oeis.org

0, 2, 2, 2, 2, 4, 2, 2, 6, 2, 2, 24, 7, 2, 2, 3, 2, 2, 2, 4, 4, 2, 11, 2, 2, 8, 4, 2, 12, 4, 2, 2, 8, 3, 2, 2, 4, 2, 2, 38, 130, 4, 4, 4, 2, 3, 2, 4, 747, 3, 4, 2, 10, 2, 3, 17, 10, 13, 2, 2, 2, 6, 42, 2, 3, 2, 6, 2, 10, 2, 4, 4, 2, 16, 50, 3, 9, 2, 22, 25

Offset: 1

Robert Price, Mar 02 2015

nonn

Robert Price, Table of n, a(n) for n = 1..143

Cf. A084712, A084713, A084714, A079706, A138066, A255707.

lst = {0}; For[n = 2, n ≤ 143, n++, For[k = 2, k >= 1, k++, If[PrimeQ[(2*n - 1)^k - 2], AppendTo[lst, k]; Break[]]]]; lst
lnk[n_]:=Module[{k=2,c=2n-1},While[!PrimeQ[c^k-2],k++];k]; Join[{0}, Array[ lnk,80,2]] (* Harvey P. Dale, Jul 24 2017 *)

A253178 Least k>=1 such that 2*A007494(n)^k+1 is prime.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 47, 1, 1, 1, 1, 2, 1, 2, 1, 1, 3, 1, 1, 1, 2729, 1, 1, 2, 1, 2, 175, 1, 1, 1, 1, 1, 1, 3, 3, 3, 43, 1, 1, 2, 1, 1, 3, 2, 1, 1, 3, 1, 11, 1, 1, 4, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 192275, 2, 1233, 1, 3, 5, 51, 1, 1, 1, 1, 286, 1, 1, 755, 2, 1, 4, 1, 6, 1, 2

Offset: 1

Eric Chen, Mar 20 2015

If n == 1 (mod 3), then for every positive integer k, 2*n^k+1 is divisible by 3 and cannot be prime (unless n=1). Thus we restrict the domain of this sequence to A007494 (n which is not in the form 3j+1).
Conjecture: a(n) is defined for all n.
a(145) > 200000, a(146) .. a(156) = {1, 1, 66, 1, 4, 3, 1, 1, 1, 1, 6}, a(157) > 100000, a(158) .. a(180) = {2, 1, 2, 11, 1, 1, 3, 321, 1, 1, 3, 1, 2, 12183, 5, 1, 1, 957, 2, 3, 16, 3, 1}.
a(n) = 1 if and only if n is in A144769.

Eric Chen, Table of n, a(n) for n = 1..144

Cf. A138066, A138067, A255707, A250200, A119624, A119591, A040076, A046067.

A007494[n_] := 2n - Floor[n/2];
Table[k=1; While[!PrimeQ[2*A007494[n]^k+1], k++]; k, {n, 1, 144}]

a007494(n) = n+(n+1)>>1;
a(n) = for(k=1, 2^24, if(ispseudoprime(2*a007494(n)^k+1),return(k)));

a(n) = A119624(A007494(n)).

A138067 Least k > 1 such that (2n-1)^k + 2 is prime, or 0 if no such number exists.

Original entry on oeis.org

2, 2, 3, 0, 2, 5, 0, 2, 105, 0, 2, 11, 0, 5, 3, 0, 2, 15, 0, 2, 9, 0, 2, 113, 0, 5, 7, 0, 2, 27, 0, 3, 3, 0, 3, 3, 0, 12, 61, 0, 2, 3, 0, 4, 255, 0, 8, 63, 0, 2, 9, 0, 2, 3473, 0, 2, 3, 0, 2, 15, 0, 2, 87, 0, 3, 23, 0, 36, 1861, 0, 4, 3, 0, 2, 5, 0, 3, 7, 0, 136, 425, 0, 11

Offset: 1

Alexander Adamchuk, Mar 02 2008

a(3n+1) = 0 for n > 0.

a(84) > 100000. - Ray Chandler, Aug 10 2011

Cf. A084713 (smallest prime of the form (2n-1)^k + 2, or 0 if no such number exists).
Cf. A138066 (least k > 0 such that (2n-1)^k + 2 is prime, or 0 if no such number exists).
Cf. A051783 (k such that 3^k + 2 is prime).
Cf. A087885 (k such that 5^k + 2 is prime).
Cf. A090649, A109076, A113480, A138048, A138049, A138050, A138051, A087886, A113481.

a(54)-a(83) from Donovan Johnson, Oct 29 2008

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A255707 Least number k > 0 such that (2*n-1)^k - 2 is prime, or 0 if no such number exists.

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A250200 Least number k>1 such that (2n-1)^k - 2 is prime, or 0 if no such number exists.

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A253178 Least k>=1 such that 2*A007494(n)^k+1 is prime.

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A138067 Least k > 1 such that (2n-1)^k + 2 is prime, or 0 if no such number exists.

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