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

1,1

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, ...

Links

Table of n, a(n) for n=1..48.

Example

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).

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

Crossrefs

Cf. A005235.

Sequence in context: A068863 A284146 A376236 * A087521 A078403 A129945

Adjacent sequences: A317476 A317477 A317478 * A317480 A317481 A317482

Keyword

nonn

Author

Amiram Eldar, Jul 29 2018

Status

approved