A118122 Least prime of level 2n-1 (cf. A117563).

5, 11, 17, 509, 29, 83, 41, 79, 887, 59, 109, 71, 331, 193, 383, 190717, 101, 107, 787, 277, 1129, 911, 137, 1181, 149, 463, 1013, 839, 1087, 179, 433, 191, 197, 4093, 349, 503, 2423, 227, 701, 239, 5378731, 587, 601, 439, 269, 6491, 281, 1621, 877, 499

Offset

1,1

Links

Table of n, a(n) for n=1..50.

Formula

Levels of primes are defined in A117563. Conjecture: there are an infinite number of prime members at each level.

Example

The first occurrence of 1 in A117563 is a(3) which implies the third prime which is 5.
The first occurrence of 3 in A117562 is a(5) which implies the fifth prime which is 11.
The first occurrence of 5 in A117562 is a(7) which implies the seventh prime which is 17, etc.

Mathematica

f[n_] := If[n == 1, 0, Block[{p = Prime@n, np = Prime[n + 1]}, (2p - np)/Min@Select[Divisors[2p - np], # >= np - p &]]]; t = Table[0, {100}]; Do[a = (f@n + 1)/2; If[a < 101 && t[[a]] == 0, t[[a]] = Prime@n; Print[{a, n, Prime@n}]], {n, 10^6}]

Crossrefs

Cf. A117078, A117563, A117873, A117874, A118481, A118508.

Sequence in context: A294135 A265851 A326716 * A314256 A314257 A314258

Adjacent sequences: A118119 A118120 A118121 * A118123 A118124 A118125

Keyword

nonn

Author

Rémi Eismann and Robert G. Wilson v, May 12 2006

Status

approved