The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A141345 Distance from the n-th highly composite number, A002182(n), to the next prime. 6
 1, 1, 1, 1, 1, 5, 1, 5, 1, 7, 1, 1, 7, 7, 13, 17, 13, 1, 11, 1, 11, 1, 1, 19, 13, 1, 11, 1, 17, 1, 29, 13, 13, 1, 1, 17, 13, 23, 17, 19, 17, 17, 19, 1, 19, 23, 37, 53, 1, 17, 29, 43, 29, 1, 19, 19, 1, 23, 23, 1, 41, 41, 1, 53, 29, 19, 19, 23, 23, 47, 29, 23, 37, 1, 59, 71, 41, 1, 29, 37 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS It appears that (1) every term is either 1 or a prime and (2) every prime greater than 3 appears. Note that a prime can occur only a finite number of times. Similar to Fortune's conjecture (A005235) and McEachen's conjecture (A117825). The arithmetic mean of a(n)/log(A002182(n)) for the terms 3..10000 is 1.513, i.e., a rough approximation is given by a(n) ~ log(A002182(n)^(3/2)). - A.H.M. Smeets, Dec 02 2020 LINKS T. D. Noe, Table of n, a(n) for n=1..10000 MATHEMATICA With[{s = Array[DivisorSigma[0, #] &, 10^6]}, Map[NextPrime[#] - # &@ FirstPosition[s, #][[1]] &, Union@ FoldList[Max, s]]] (* or *) Map[NextPrime[#] - # &, Import["https://oeis.org/A002182/b002182.txt", "Data"][[1 ;; 80, -1]] ] (* Michael De Vlieger, Dec 11 2020 *) CROSSREFS Sequence in context: A251417 A100947 A096940 * A318664 A329031 A264483 Adjacent sequences:  A141342 A141343 A141344 * A141346 A141347 A141348 KEYWORD nonn AUTHOR T. D. Noe, Jun 26 2008 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 August 3 21:13 EDT 2021. Contains 346441 sequences. (Running on oeis4.)