

A141345


Distance from the nth 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
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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



