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A343729
a(n) is the smallest number that starts a run of exactly n consecutive integers that are neither primes nor semiprimes.
0
8, 27, 98, 342, 242, 6092, 3174, 2870, 2522, 16023, 26604, 114359, 41780, 74492, 39344, 463162, 104660, 248408, 517422, 923723, 506510, 1930824, 584214, 2560178, 4036968, 4570412, 4552364, 7879254, 4417814, 27841052, 5167588, 13683035, 9725108, 47735343
OFFSET
1,1
EXAMPLE
a(5) = 242 because 241 is a prime, 247=13*19 is a semiprime, none of the 5 consecutive integers between them are primes or semiprimes (242 = 2*11^2, 243 = 3^5, 244 = 2^2*61, 245 = 5*7^2, and 246 = 2*3*41), and there is no smaller run of exactly 5 consecutive integers that are neither prime nor semiprime.
MATHEMATICA
Module[{nn=48*10^6, lst}, lst=Table[Which[PrimeQ[n], 1, PrimeOmega[n]==2, 1, True, 0], {n, nn}]; Flatten[Table[SequencePosition[lst, Join[{1}, PadRight[{}, n, 0], {1}], 1], {n, 34}], 1]][[;; , 1]]+1 (* Harvey P. Dale, May 30 2024 *)
CROSSREFS
Sequence in context: A343323 A079712 A056598 * A343283 A126163 A307117
KEYWORD
nonn
AUTHOR
Jon E. Schoenfield, May 22 2021
EXTENSIONS
Corrected by Harvey P. Dale, May 30 2024
STATUS
approved