A101940 Numbers n with omega(n) < omega of 3 nearest larger and 3 nearest smaller neighbors.

37, 53, 89, 97, 113, 121, 157, 163, 173, 211, 223, 233, 251, 263, 277, 289, 293, 307, 317, 331, 337, 343, 353, 367, 373, 379, 383, 389, 397, 401, 409, 439, 443, 449, 457, 467, 479, 487, 491, 499, 503, 529, 541, 547, 557, 563, 577, 587

Offset

1,1

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Example

37 is in the sequence because it has one unique prime factor (itself), whereas 34, 35, 36, 38, 39 and 40 each have more.

Mathematica

For[i=1, i<1000, If[And[Length[FactorInteger[i-3]] > Length[FactorInteger[i]], Length[FactorInteger[i-2]]>Length[FactorInteger[i]], Length[FactorInteger[i-1]]>Length[FactorInteger[i]], Length[FactorInteger[i+1]]> Length[FactorInteger[i]], Length[FactorInteger[i+2]]> Length[FactorInteger[i]], Length[FactorInteger[i+3]]> Length[FactorInteger[i]]], Print[i]]; i++ ]
Select[Range[6500], PrimeNu[#] < Min[PrimeNu[# - 1], PrimeNu[# - 2], PrimeNu[# - 3], PrimeNu[# + 1], PrimeNu[# + 2], PrimeNu[# + 3]] &] (* G. C. Greubel, May 21 2017 *)

Crossrefs

Cf. A001221, A101934, A101938.

Sequence in context: A302720 A304358 A214755 * A330339 A036540 A225214

Adjacent sequences: A101937 A101938 A101939 * A101941 A101942 A101943

Keyword

easy,nonn

Author

Neil Fernandez, Dec 21 2004

Status

approved