Records of the total number of prime factors in the numbers between consecutive primes.
4, 1, 6, 2, 8, 3, 14, 4, 20, 5, 32, 6, 54, 7, 74, 8, 90, 9, 114, 14, 212, 15, 294, 16, 524, 20, 888, 25, 1130, 27, 1328, 37, 4298, 38, 4832, 39, 5352, 40, 5592, 41, 8468, 45, 12854, 49, 15684, 56, 19610, 64, 25472, 66, 31398, 89, 134514, 90, 155922, 114
1
We show the pair of numbers: the first composite number where the record occurs and the record value. The occurrences of records in A052297. See S000335 and S000336 for the separate sequences.
T. D. Noe, Plot of 80 terms
T. D. Noe, Table of 80 terms
(Mma) t = {{0, 0}}; Do[m = 1; n = p + 1; While[! PrimeQ[n], m = m*n; n++]; s = Length[FactorInteger[m]]; If[s > t[[-1, 2]], AppendTo[t, {p + 1, s}]], {p, Prime[Range[2, 10000]]}]; t = Rest[t]
nonn,hard
T. D. Noe, Nov 12 2014