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
Keywords
Examples
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.
Programs
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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}]
Formula
Levels of primes are defined in A117563. Conjecture: there are an infinite number of prime members at each level.