This site is supported by donations to The OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A319852 Difference between 3^n and the product of primes less than or equal to n. 2
 0, 2, 7, 21, 75, 213, 699, 1977, 6351, 19473, 58839, 174837, 529131, 1564293, 4752939, 14318877, 43016691, 128629653, 386909979, 1152561777, 3477084711, 10450653513, 31371359919, 93920085957, 282206443611, 847065516573, 2541642735459, 7625374392117, 22876569362091 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS From Rosser (1941), it seems that the tightest possible upper bound is somewhere between e^n and 2.83^n. Therefore 3^n is the best possible upper bound with an integer base and integer exponent. - Alonso del Arte, Oct 22 2018 LINKS Barkley Rosser, "Explicit Bounds for Some Functions of Prime Numbers", Amer. J. Math., 1941, 63 (1) p. 228, Lemma 21. J. Barkley Rosser, Lowell Schoenfeld, Approximate formulas for some functions of prime numbers, Illinois J. Math. 6 1962, 64-94. FORMULA a(n) = 3^n - n#, where n# = A034386(n) is the product of the primes less than or equal to n. EXAMPLE 3^5 = 243. The primes less than or equal to 5 are: 2, 3, 5. Then 2 * 3 * 5 = 30 and hence a(5) = 243 - 30 = 213. MATHEMATICA Table[3^n - Times@@Select[Range[n], PrimeQ], {n, 0, 26}] PROG (PARI) a(n) = 3^n-factorback(primes(primepi(n))) \\ David A. Corneth, Oct 22 2018 CROSSREFS Cf. A000244, A034386, A319857. Sequence in context: A274203 A220726 A127540 * A060900 A305850 A151289 Adjacent sequences:  A319849 A319850 A319851 * A319853 A319854 A319855 KEYWORD nonn AUTHOR Alonso del Arte, Sep 29 2018 EXTENSIONS Many thanks to Amiram Eldar for several bibliographic citations on this topic. STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 19 04:52 EDT 2019. Contains 327187 sequences. (Running on oeis4.)