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A317479
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Primes with record values of corresponding Fortunate numbers (A005235).
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0
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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
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OFFSET
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1,1
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COMMENTS
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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, ...
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LINKS
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EXAMPLE
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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).
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MATHEMATICA
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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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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