A343729 a(n) is the smallest number that starts a run of exactly n consecutive integers that are neither primes nor semiprimes.

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

Links

Table of n, a(n) for n=1..34.

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

Cf. A045881, A340735.

Sequence in context: A343323 A079712 A056598 * A343283 A126163 A307117

Adjacent sequences: A343726 A343727 A343728 * A343730 A343731 A343732

Keyword

nonn

Author

Jon E. Schoenfield, May 22 2021

Extensions

Corrected by Harvey P. Dale, May 30 2024

Status

approved