A363998 -id:A363998 - cp's OEIS frontend

A363999 Numbers of the form |2^i - 3^j|, for i >= 1, j >= 1.

1, 5, 7, 11, 13, 17, 19, 23, 25, 29, 37, 47, 49, 55, 61, 65, 73, 77, 79, 101, 115, 119, 125, 139, 175, 179, 211, 217, 227, 229, 235, 239, 241, 247, 253, 269, 295, 431, 473, 485, 503, 509, 601, 665, 697, 713, 721, 725, 727, 781, 943, 997, 1015, 1021, 1163

Offset: 1

Clark Kimberling, Jul 30 2023

nonn

Cf. A014121, A363998, A364000, A364001.

A364001 Primes of the form |2^i - 3^j|, i >= 1, j >= 1.

Original entry on oeis.org

5, 7, 11, 13, 17, 19, 23, 29, 37, 47, 61, 73, 79, 101, 139, 179, 211, 227, 229, 239, 241, 269, 431, 503, 509, 601, 727, 997, 1021, 1163, 1319, 1931, 2039, 2179, 3299, 3853, 4093, 4513, 6529, 6553, 7949, 8111, 11491, 14197, 16141, 16381, 19427, 19681, 32687

Offset: 1

Clark Kimberling, Aug 09 2023

nonn

Cf. A014121, A192110, A192111, A363998.

z = 500;
t = Table[Abs[2^i - 3^j], {i, 1, z}, {j, 1, z}];
u = Sort[Flatten[t]];
v = Union[u] ; (* A363999 *)
w = (v - 1)/2 ;  (* A364000 *)
Intersection[v, Prime[Range[200000]]]  (* this sequence *)

A363997 Position in A088732 of the n-th prime.

Original entry on oeis.org

1, 2, 3, 4, 6, 7, 9, 5, 10, 8, 12, 15, 16, 19, 14, 21, 11, 22, 24, 18, 27, 20, 30, 31, 17, 34, 36, 37, 40, 28, 42, 45, 49, 51, 13, 26, 52, 54, 55, 38, 57, 32, 64, 33, 44, 66, 23, 46, 69, 35, 70, 25, 50, 75, 76, 79, 41, 82, 56, 84, 29, 58, 87, 60, 90, 91, 48

Offset: 1

Clark Kimberling, Jul 11 2023

nonn

Every positive integer occurs exactly once.

			a(7) = 5 because the 7th prime, 19, is the 5th term in A088732.

Cf. A000040, A088732, A038780, A363998.

z= 200; t = Table[k = 1; While[p = n + k*(n + 1); ! PrimeQ[p], k++];
  p, {n, 0, z}];   (* A088732, after Frank M Jackson *)
Flatten[Table[Position[t, Prime[n]], {n, 1, z}]]  (* this sequence *)

cp's OEIS Frontend

A363999 Numbers of the form |2^i - 3^j|, for i >= 1, j >= 1.

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A364001 Primes of the form |2^i - 3^j|, i >= 1, j >= 1.

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A363997 Position in A088732 of the n-th prime.

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Mathematica