A317479 Primes with record values of corresponding Fortunate numbers (A005235).

2, 3, 5, 7, 11, 23, 29, 31, 41, 47, 61, 79, 83, 101, 137, 193, 199, 337, 349, 557, 677, 977, 1069, 1087, 1279, 1483, 1579, 1877, 2053, 2591, 2713, 2843, 3359, 3823, 4243, 6011, 7393, 7411, 7459, 8179, 8389, 15313, 18287, 19463, 21323, 22153, 23011, 27067

Offset: 1

Author

Amiram Eldar, Jul 29 2018

Keywords

• nonn

Comments

The corresponding record values of the Fortunate numbers are 3, 5, 7, 13, 23, 37, 61, 67, 71, 107, 109, 151, 197, 233, 643, 751, 773, 883, 1381, 1423, 2087, 2243, 2357, 3559, 3739, 5323, 5689, 6271, 7187, 7309, 8713, 11069, 11411, 19699, 20249, 25621, 28351, 28817, 32443, 39769, 59981, 78059, 82339, 86293, 89657, 90127, 101021, 129589, ...

Primes that are in both of these 2 sequences: 3, 5, 7, 23, 61, ...

Examples

			23 is in the sequence since the prime next to 23#+1 is 23#+37 and 37 is larger than all the Fortunate numbers before it (3, 5, 7, 13, 23, 17, 19, 23).
		

Crossrefs

Cf. A005235.

Programs

Mathematica

primorial[n_] := Times @@ Prime[Range[n]]; gap[n_] := NextPrime[n + 1] - n; fort[n_] := gap[primorial[n]]; fm=0; s={}; Do[f = fort[n]; If[f > fm, AppendTo[s, Prime[n]]; fm = f], {n, 1, 30}]; s